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Chapter: 4 -Problem: 9 >> Three monkeys A, B, and C weighing 20, 25, and 15 lb, respectively, are climbing up and down the rope suspended from D. At the instant represented, A is descending the rope with an acceleration of 5 ft/sec2, and C is pulling himself up with an acceleration of 3 ft/sec2. Monkey B is climbing up with a constant speed of 2 ft/sec. Treat the rope and monkeys as a complete system and calculate the tens
Answer Preview: The tension in the rope at D can be calculated by considering the forces acting on the system The fo…

, Chapter: 7 -Problem: 97 >> A car makes a turn to the right on a level road. Determine whether the normal reaction under the right rear wheel is increased or decreased as a result of the gyroscopic effect of the precessing wheels.
Answer Preview: The normal reaction under the right rear wheel is increased as a result of the gyroscopic …

, Chapter: 8 -Problem: 137 >> The 4-kg mass is suspended by the spring of stiffness k = 350 N/m and is initially at rest in the equilibrium position. If a downward force F = Ct is applied to the body and reaches a value of 40 N when t = 1 s, derive the differential equation of motion, obtain its solution, and plot the displacement y in millimeters as a function of time during the first second. Damping is negligible.
Answer Preview: Differential Equation of Motion The differential equation of motion for this system can be derived u…

, Chapter: 3 -Problem: 204 >> The ice-hockey puck with a mass of 0.20 kg has a velocity of 12 m/s before being struck by the hockey stick. After the impact the puck moves in the new direction shown with a velocity of 18 m/s. If the stick is in contact with the puck for 0.04 s, compute the magnitude of the average force F exerted by the stick on the puck during contact, and find the angle ? made by F with the x-direction.
Answer Preview: The magnitude of the average force F exerted by the stick on the puck during con…

, Chapter: 4 -Problem: 95 >> Each of the identical steel balls weighs 4 lb and is fastened to the other two by connecting bars of negligible weight and unequal length. In the absence of friction at the supporting horizontal surface, determine the initial acceleration a? of the mass center of the assembly when it is subjected to the horizontal force F = 20 lb applied to the supporting ball. The assembly is initially at rest in
Answer Preview: To determine the initial acceleration of the mass center of the assembly we can analyze the forces acting on it and apply Newton s second law of motio…

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, Chapter: 3 -Problem: 92 >> The uniform slender rod of length L, mass m, and cross-sectional area A is rotating in a horizontal plane about the vertical central axis O-O at a constant high angular velocity ?. By analyzing the horizontal forces on the accelerating differential element shown, derive an expression for the tensile stress ? in the rod as a function of r. The stress, commonly referred to as centrifugal stress, equ
Answer Preview: To derive an expression for the tensile stress in the rod as a function of r we will analyze the hor…

, Chapter: 3 -Problem: 151 >> The system is released from rest with the spring initially stretched 2 in. Calculate the velocity of the 100-lb cylinder after it has dropped 6 in. Also determine the maximum drop distance of the cylinder. Neglect the mass and friction of the pulleys. Transcribed Image Text: k = 5 lb/in. 100 lb ww
Answer Preview: The velocity of the 100 lb cylinder after it has dropped 6 in can be calculated using the equati…

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, Chapter: 9 -Problem: 67 >> The aluminium casting consists of a 6-in. cube with a 4-in. cubical recess. Calculate the products of inertia of the casting about the axes shown. Transcribed Image Text: 4" 6" 4" 6" 6
Answer Preview: To calculate the products of inertia of the casting about the axes shown we ll need to find the moment of inertia for each axis separately and then us…

, Chapter: 3 -Problem: 97 >> The spring is unstretched at the position x = 0. Under the action of a force P, the cart moves from the initial position x1 = ?6 in. to the final position x2 = 3 in. Determine (a) The work done on the cart by the spring (b) The work done on the cart by its weight. Transcribed Image Text: Unstretched
Answer Preview: Position is how a person or thing is placed or an opinion or where a pers…

, Chapter: 3 -Problem: 184 >> The 15 200-kg lunar lander is descending onto the moon’s surface with a velocity of 2 m/s when its retro-engine is fired. If the engine produces a thrust T for 4 s which varies with time as shown and then cuts off, calculate the velocity of the lander when t = 5 s, assuming that it has not yet landed. Gravitational acceleration at the moon’s surface is 1.62 m/s2.
Answer Preview: GIVEN m 15200 kg v 1 2 m s t 5 sec g 1 62 m s 2 Requi…

, Chapter: 4 -Problem: 100 >> When only the air of a sand-blasting gun is turned on, the force of the air on a flat surface normal to the stream and close to the nozzle is 20 N. With the nozzle in the same position, the force increases to 30 N when sand is admitted to the stream. If sand is being consumed at the rate of 4.5 kg/min, calculate the velocity v of the sand particles as they strike the surface.
Answer Preview: Assuming the density of sand is 2600 kg m 3 we can calculate the mass flow r…

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, Chapter: 3 -Problem: 24 >> The coefficient of static friction between the flat bed of the truck and the crate it carries is 0.30. Determine the minimum stopping distance s which the truck can have from a speed of 70 km / h with constant deceleration if the crate is not to slip forward. Transcribed Image Text: -3 m-
Answer Preview: The coefficient of static friction between the flat bed of the truck and the crate it carries is …

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, Chapter: 5 -Problem: 5 >> When switched on, the grinding machine accelerates from rest to its operating speed of 3450 rev/min in 6 seconds. When switched off, it coasts to rest in 32 seconds. Determine the number of revolutions turned during both the startup and shutdown periods. Assume uniform angular acceleration in both cases.
Answer Preview: The number of revolutions turned during the startup period can b…

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, Chapter: 3 -Problem: 132 >> It is experimentally determined that the drive wheels of a car must exert a tractive force of 560 N on the road surface in order to maintain a steady vehicle speed of 90 km/h on a horizontal road. If it is known that the overall drivetrain efficiency is em = 0.70, determine the required motor power output P
Answer Preview: The required motor power output P can be calcul…

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, Chapter: 3 -Problem: 65 >> Calculate the necessary rotational speed N for the aerial ride in an amusement park in order that the arms of the gondolas will assume an angle ? = 60° with the vertical. Neglect the mass of the arms to which the gondolas are attached and treat each gondola as a particle. Transcribed Image Text: F3
Answer Preview: Apply the force equilibrium condition on x and y direction and acquire the angular speed Then use the relation of associategular speed to get the mand…

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, Chapter: 2 -Problem: 81 >> If the launch speed of the golf ball of the previous problem remains v0 = 115 mi/hr, what launch angle ? will put the first impact point of the ball closest to the pin? How far from the pin is this impact point?
Answer Preview: Almost everything humans do from growing food to man…

, Chapter: 5 -Problem: 2 >> The circular sector rotates about a fixed axis through point O with angular velocity ? = 2 rad/s and angular acceleration ? = 4 rad/s2 with directions as indicated in the figure. Determine the instantaneous velocity and acceleration of point A. Transcribed Image Text: y --x 15° 150 0.3 m 'A
Answer Preview: The instantaneous velocity of point A can be determined …

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, Chapter: 3 -Problem: 115 >> The position vector of a particle is given by r = 8ti + 1.2t2j ? 0.5(t3 ? 1)k, where t is the time in seconds from the start of the motion and where r is expressed in meters. For the condition when t = 4 s, determine the power P developed by the force F = 40i ? 20j ? 36k N which acts on the particle.
Answer Preview: F 8t 1 2 tj 0 5 t 1 k F 401 201 36k Power Work dW F d dw dt dt dW dt wo…

, Chapter: 2 -Problem: 95 >> A projectile is launched with speed v0 from point A. Determine the launch angle ? which results in the maximum range R up the incline of angle ? (where 0 ? ? ? 90°). Evaluate your results for ? = 0, 30°, and 45°. Transcribed Image Text: ? B Ta A R Problem 2/95
Answer Preview: For a projectile launched with speed v0 from point A the launch angle that results in the max…

, Chapter: 5 -Problem: 33 >> The hydraulic cylinder D is causing the distance OA to increase at the rate of 2 in./sec. Calculate the velocity of the pin at C in its horizontal guide for the instant when ? = 50o. Transcribed Image Text: AO 6". 6". B D 6" C
Answer Preview: The velocity of the pin at C can be calculated using the equation for velocity of a …

, Chapter: 7 -Problem: 139 >> A top consists of a ring of mass m = 0.52 kg and mean radius r = 60 mm mounted on its central pointed shaft with spokes of negligible mass. The top is given a spin velocity of 10 000 rev/min and released on the horizontal surface with the point O remaining in a fixed position. The axis of the top is seen to make an angle of 15° with the vertical as it precesses. Determine the number N of precessio
Answer Preview: The number of precession cycles per minute N can be calculated using the following equation N 2r T w…

, Chapter: 8 -Problem: 113 >> The 12-kg block is supported by the two 5-kg links with two torsion springs, each of constant kT = 500 N ? m/rad, arranged as shown. The springs are sufficiently stiff so that stable equilibrium is established in the position shown. Determine the natural frequency ƒn for small oscillations about this equilibrium position.
Answer Preview: To determine the natural frequency n for small oscillations about the equilibrium position in this system we need to consider the effect of gravity on …

, Chapter: 3 -Problem: 206 >> A spacecraft in deep space is programmed to increase its speed by a desired amount ?v by burning its engine for a specified time duration t. Twenty-five percent of the way through the burn, the engine suddenly malfunctions and thereafter produces only half of its normal thrust. What percent n of ?v is achieved if the rocket motor is fi red for the planned time t? How much extra time t? would the r
Answer Preview: The percent of v achieved in the planned time t can be calculat…

, Chapter: 2 -Problem: 65 >> Prove the well-known result that, for a given launch speed v0, the launch angle ? = 45° yields the maximum horizontal range R. Determine the maximum range.
Answer Preview: Hence the required value of maximum height is u2sin…

, Chapter: 5 -Problem: 43 >> Vertical motion of the work platform is controlled by the horizontal motion of pin A. If A has a velocity v0 to the left, determine the vertical velocity v of the platform for any value of ?. Transcribed Image Text: L/2 L/2 L/2 e L12 A
Answer Preview: Ans In triangle ABC BAC BCA ABC 180 180 180 2 Now in triangle ABD sin BD AB sin h L 2 h L …

, Chapter: 7 -Problem: 140 >> The uniform circular disk of 4-in. radius and small thickness weighs 8 lb and is spinning about its y?- axis at the rate N = 300 rev/min with its plane of rotation tilted at a constant angle ? = 20° from the vertical x-z plane. Simultaneously, the assembly rotates about the fixed z-axis at the rate p = 60 rev/min. Calculate the angular momentum HO of the disk alone about the origin O of the x-y-z
Answer Preview: The angular momentum HO of the disk about the origin O can be calculated using the following equatio…

, Chapter: 8 -Problem: 118 >> The quarter-circular sector of mass m and radius r is set into small rocking oscillation on the horizontal surface. If no slipping occurs, determine the expression for the period ? of each complete oscillation.
Answer Preview: To determine the expression for the period of each complete oscillation of the quarter circular sect…

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, Chapter: 2 -Problem: 64 >> With what minimum horizontal velocity u can a boy throw a rock at A and have it just clear the obstruction at B? Transcribed Image Text: 40 m A B 26 m 16 m Problem 2/64
Answer Preview: 26m 1 S Ut at 1 2 t 1 428 S U Rock is thrown horizontally Hence for vertical motion Initial velocity is zero UT 0 The vertical distance required to just cross Point B S 26 16 10m 10 x 9 81 x t 40m The minimum horizontal …

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, Chapter: 8 -Problem: 9 >> Determine the period ?  for the system shown. The cable is always taut, and the mass and friction of the pulley are to be neglected. Transcribed Image Text: m
Answer Preview: The period of a system is the time it takes for the system to complete one full cycle In this case t…

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, Chapter: 2 -Problem: 131 >> A car P travels along a straight road with a constant speed v = 65 mi/ hr. At the instant when the angle ? = 60°, determine the values of r? in ft/sec and ?? in deg/sec. Transcribed Image Text: P 100' y Problem 2/131
Answer Preview: 100 30 To Find and ii 0 60 cos P has velocity V 65 mi hr This velocity can be resolved …

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, Chapter: 3 -Problem: 210 >> A tennis player strikes the tennis ball with her racket while the ball is still rising. The ball speed before impact with the racket is v1 = 15 m/s and after impact its speed is v2 = 22 m/s, with directions as shown in the figure. If the 60-g ball is in contact with the racket for 0.05 s, determine the magnitude of the average force R exerted by the racket on the ball. Find the angle ? made by R w
Answer Preview: v1 15 m s v2 22 m s m 60 gm 0 06 kg t 0 05 s Linear momentam in x d…

, Chapter: 2 -Problem: 94 >> A projectile is launched from point A and lands on the same level at D. Its maximum altitude is h. Determine and plot the fraction ƒ2 of the total flight time that the projectile is above the level ƒ1h, where ƒ1 is a fraction which can vary from zero to 1. State he value of ƒ2 for ƒ1 = 3/4 . Transcribed Image Text:
Answer Preview: graph nature will be like this Ignore the numerical values …

, Chapter: 4 -Problem: 101 >> A two-stage rocket is fired vertically up and is above the atmosphere when the first stage burns out and the second stage separates and ignites. The second stage carries 1200 kg of fuel and has an empty mass of 200 kg. Upon ignition the second stage burns fuel at the rate of 5.2 kg/s and has a constant exhaust velocity of 3000 m/s relative to its nozzle. Determine the acceleration of the second st
Answer Preview: The acceleration of the second stage 60 seconds after ignition is 1037 4 m s2 The maximum accelerati…

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, Chapter: 8 -Problem: 110 >> The rotational axis of the turntable is inclined at an angle a from the vertical. The turntable shaft pivots freely in bearings which are not shown. If a small block of mass m is placed a distance r from point O, determine the natural frequency wn for small rotational oscillations through the angle ?. The mass moment of inertia of the turntable about the axis of its shaft is I.
Answer Preview: To determine the natural frequency w n for small rotational oscillations of the turntable through th…

, Chapter: 3 -Problem: 130 >> The system is released from rest with no slack in the cable and with the spring unstretched. Determine the distance s traveled by the 4-kg cart before it comes to rest (a) If m approaches zero (b) If m = 3 kg. Assume no mechanical interference and no friction, and state whether the distance traveled is up or down the incline.
Answer Preview: a It is given that a system is released from rest where no slack is attached to the cab…

, Chapter: 2 -Problem: 68 >> A fi reworks show is choreographed to have two shells cross paths at a height of 160 feet and explode at an apex of 200 feet under normal weather conditions. If the shells have a launch angle ? = 60° above the horizontal, determine the common launch speed v0 for the shells, the separation distance d between the launch points A and B, and the time from launch at which the shells explode.
Answer Preview: The common launch speed v0 for the shells can be determined using the equa…

, Chapter: 4 -Problem: 104 >> A jet of fresh water under pressure issues from the 3/4-in.-diameter fixed nozzle with a velocity v = 120 ft/sec and is diverted into the two equal streams. Neglect any energy loss in the streams and compute the force F required to hold the vane in place. Transcribed Image Text: 30° A F 30°
Answer Preview: The force F required to hold the vane in p…

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, Chapter: 3 -Problem: 190 >> The 600,000-lb jet airliner has a touchdown velocity v = 120 mi/hr directed ? = 0.5° below the horizontal. The touchdown process of the eight main wheels takes 0.6 sec to complete. Treat the aircraft as a particle and estimate the average normal reaction force at each wheel during this 0.6-sec process, during which tires deflect, struts compress, etc. Assume that the aircraft lift equals the aircr
Answer Preview: The average normal reaction force at each wheel during the touchdown process can be est…

, Chapter: 2 -Problem: 135 >> Rotation of bar OA is controlled by the lead screw which imparts a horizontal velocity v to collar C and causes pin P to travel along the smooth slot. Determine the values of r? and ??, where r = OP, if h = 160 mm, x = 120 mm, and v = 25 mm/s at the instant represented. Transcribed Image Text: h C A
Answer Preview: r v cos v sin r Using the given value…

, Chapter: 4 -Problem: 73 >> The mass m of a raindrop increases as it picks up moisture during its vertical descent through still air. If the air resistance to motion of the drop is R and its downward velocity is v, write the equation of motion for the drop and show that the relation ?F = d(mv)/dt is obeyed as a special case of the variable-mass equation.
Answer Preview: The equation of motion for a raindrop in still air is given by Newton s second law of motion which s…

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, Chapter: 8 -Problem: 77 >> The uniform sector has mass m and is freely hinged about a horizontal axis through point O. Determine the equation of motion of the sector for large-amplitude vibrations about the equilibrium position. State the period  ? for small oscillations about the equilibrium position if r = 325 mm and ? = 45°. Transcribed Image Tex
Answer Preview: To determine the equation of motion of the sector for large amplitude vibrations about the equilibrium position we need to use the principle of conser…

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, Chapter: 2 -Problem: 122 >> A football player releases a ball with the initial conditions shown in the figure. Determine the radius of curvature ? of the path and the time rate of change v? of the speed at times t = 1 sec and t = 2 sec, where t = 0 is the time of release from the quarterback’s hand. Transcribed Image Text: Vo
Answer Preview: The radius of curvature of a parabolic path of an object …

, Chapter: 5 -Problem: 3 >> The angular velocity of a gear is controlled according to ? = 12 ? 3t2 where ?, in radians per second, is positive in the clockwise sense and where t is the time in seconds. Find the net angular displacement ?? from the time t = 0 to t = 3 s. Also find the total number of revolutions N through which the gear turns during the 3 seconds.
Answer Preview: The angular velocity of the gear is given by the equation 12 3t2 where is …

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, Chapter: 3 -Problem: 136 >> The nest of two springs is used to bring the 0.5-kg plunger A to a stop from a speed of 5 m/s and reverse its direction of motion. The inner spring increases the deceleration, and the adjustment of its position is used to control the exact point at which the reversal takes place. If this point is to correspond to a maximum deflection ? = 200 mm for the outer spring, specify the adjustment of the i
Answer Preview: To solve this problem we need to first determine the deceleration of the plunger caused by the inner …

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, Chapter: 5 -Problem: 6 >> The small cart is released from rest in position 1 and requires 0.638 seconds to reach position 2 at the bottom of the path, where its center G has a velocity of 14.20 ft/sec. Determine the angular velocity ? of line AB in position 2 and the average angular velocity ?av of AB during the interval. Transcribed Image Text:
Answer Preview: angular velocit…

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, Chapter: 8 -Problem: 101 >> Determine the period ? for the uniform circular hoop of radius r as it oscillates with small amplitude about the horizontal knife edge.Solve the following problems by the energy method.
Answer Preview: Solution using the energy method The total energy of the system is the sum of the kinetic energy and …

, Chapter: 3 -Problem: 197 >> The pilot of a 90,000-lb airplane which is originally flying horizontally at a speed of 400 mi/hr cuts off all engine power and enters a 5° glide path as shown. After 120 seconds the airspeed is 360 mi/hr. Calculate the time-average drag force D (air resistance to motion along the flight path). Transcribed Image Text:
Answer Preview: D 90 000 lbs …

, Chapter: 2 -Problem: 97 >> A test car starts from rest on a horizontal circular track of 80-m radius and increases its speed at a uniform rate to reach 100 km/h in 10 seconds. Determine the magnitude a of the total acceleration of the car 8 seconds after the start. Transcribed Image Text: 80 m Problem 2/97
Answer Preview: Magnitude of total acceleration Square root radial acceleration 2 ta…

, Chapter: 5 -Problem: 38 >> Determine the acceleration of the shaft B for ? = 60° if the crank OA has an angular acceleration ?¨ = 8 rad/s2 and an angular velocity ?? = 4 rad/s at this position. The spring maintains contact between the roller and the surface of the plunger. Transcribed Image Text: ? 20 mm AO 80 mm-
Answer Preview: The term rolling contact bearings refers to the wide variety of bearings that use spherical balls or …

, Chapter: 8 -Problem: 14 >> The 4-oz slider oscillates in the fixed slot under the action of the three springs, each of stiffness k = 0.5 lb/in. If the initial conditions at time t = 0 are x0 = 0.1 in. and x?0 = 0.5 in./sec, determine the position and velocity of the slider at time t = 2 sec. What is the system period? Transcribed Image Text:
Answer Preview: Velocity v is a vector quantity that measures displacement or change in position s over the change i…

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, Chapter: 3 -Problem: 208 >> The 1.2-lb sphere is moving in the horizontal x-y plane with a velocity of 10 ft /sec in the direction shown and encounters a steady flow of air in the x-direction. If the air stream exerts an essentially constant force of 0.2 lb on the sphere in the x-direction, determine the time t required for the sphere to cross the y-axis again.
Answer Preview: The time required for the sphere to cross the y axis again can be determined by using the equation …

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, Chapter: 5 -Problem: 53 >> A variable-speed belt drive consists of the two pulleys, each of which is constructed of two cones which turn as a unit but are capable of being drawn together or separated so as to change the effective radius of the pulley. If the angular velocity ?1 of pulley 1 is constant, determine the expression for the angular acceleration ?2 = ??2 of pulley 2 in terms of the rates of change r?1 and r?2 of t
Answer Preview: Solution Step by step The answer provided below has been developed in a clear step by s…

, Chapter: 8 -Problem: 27 >> Viscous damping is added to an initially undamped spring-mass system. For what value of the damping ratio ? will the damped natural frequency wd be equal to 90 percent of the natural frequency of the original undamped system?
Answer Preview: 0 45 Explanation The damping ratio is the ratio of the damping force to the critical damping force …

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, Chapter: 3 -Problem: 141 >> The 2-kg plunger is released from rest in the position shown where the spring of stiffness k = 500 N /m has been compressed to one-half its uncompressed length of 200 mm. Calculate the maximum height h above the starting position reached by the plunger. Transcribed Image Text: 2 kg 150 mm 100 mm
Answer Preview: The maximum height h above the starting position reached by the plung…

, Chapter: 2 -Problem: 150 >> The diver leaves the platform with an initial upward speed of 2.5 m /s. A stationary camera on the ground is programmed to track the diver throughout the dive by rotating the lens to keep the diver centered in the captured image. Plot ?? and ?¨ as functions of time for the camera over the entire dive and state the values of ?? and ?¨ at the instant the diver enters the water. Treat the diver as a
Answer Preview: ANSWER To solve this problem we need to analyze the motion of the diver and the camera Let s assume the positive direction for angles and angular velo…

, Chapter: 4 -Problem: 75 >> A model rocket weighs 1.5 lb just before its vertical launch. Its experimental solid-fuel motor carries 0.1 lb of fuel, has an escape velocity of 3000 ft/sec, and burns the fuel for 0.9 sec. Determine the acceleration of the rocket at launch and its burnout velocity. Neglect aerodynamic drag and state any other assumptions.
Answer Preview: The acceleration of the rocket at launch can be calculated using Newton s Second Law of Motion which …

, Chapter: 9 -Problem: 69 >> The S-shaped piece is formed from a rod of diameter d and bent into the two semicircular shapes. Determine the products of inertia for the rod, for which d is small compared with r. Transcribed Image Text: d ??
Answer Preview: To determine the products of inertia for the rod bent into the S shaped piece we need to consider th…

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, Chapter: 3 -Problem: 149 >> The particle of mass m = 1.2 kg is attached to the end of the light rigid bar of length L = 0.6 m. The system is released from rest while in the horizontal position shown, at which the torsional spring is undeflected. The bar is then observed to rotate 30° before stopping momentarily. (a) Determine the value of the torsional spring constant kT. (b) For this value of kT, determine the speed v of th
Answer Preview: a To determine the value of the torsional spring constant kT we can use the equation for the torque …

, Chapter: 2 -Problem: 155 >> At the instant depicted in the figure, the radar station at O measures the range rate of the space shuttle P to be r? = ?12,272 ft/sec, with O considered fixed. If it is known that the shuttle is in a circular orbit at an altitude h = 150 mi, determine the orbital speed of the shuttle from this information. Transcribed Ima
Answer Preview: To solve this problem we can use the following formula for the range rate of a satellite in circular …

, Chapter: 5 -Problem: 7 >> The flywheel has a diameter of 600 mm and rotates with increasing speed about its z-axis shaft. When point P on the rim crosses the y-axis with ? = 90°, it has an acceleration given by a = ?1.8i ? 4.8j m /s2. For this instant, determine the angular velocity ? and the angular acceleration ? of the flywheel. Transcribed Imag
Answer Preview: D 600 mm n cos t cos 90 0 x n cos 0 t sino x P W o X …

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, Chapter: 2 -Problem: 80 >> A golfer is attempting to reach the elevated green by hitting his ball under a low-hanging branch in one tree A, but over the top of a second tree B. For v0 = 115 mi/hr and ? = 18°, where does the golf ball land first? Transcribed Image Text: A B 60 24 30 -70 yd- -75 yd- 10'10' yd yd 15 yd Problem 2
Answer Preview: To solve this problem we can use the equations of motion for a projectile Assuming that air resistan…

, Chapter: 5 -Problem: 20 >> Develop general expressions for the instantaneous velocity and acceleration of point A of the square plate, which rotates about a fixed axis through point O. Take all variables to be positive. Then evaluate your expressions for ? = 30°, b = 0.2 m, ? = 1.4 rad/s, and ? = 2.5 rad/s2. Transcribed Image Text:
Answer Preview: The general expressions for the instantaneous velocity and acceleration of point A of the squar…

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, Chapter: 3 -Problem: 118 >> The 15-lb cylindrical collar is released from rest in the position shown and drops onto the spring. Calculate the velocity v of the cylinder when the spring has been compressed 2 in. Transcribed Image Text: B | | A 15 lb 18" k 80 lb/in.
Answer Preview: Mass of the collar let s denote it by M 15 lb The distance between the coll…

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, Chapter: 5 -Problem: 13 >> The T-shaped body rotates about a horizontal axis through point O. At the instant represented, its angular velocity is ? = 5 rad/sec and its angular acceleration is ? = 10 rad/sec2 in the directions indicated. Determine the velocity and acceleration of (a) point A and (b) point B. Express your results in terms of components along the x- and y-axes shown.
Answer Preview: Step 1 Displacement of an object is defined as the shortest possible change in the position of an ob…

, Chapter: 8 -Problem: 38 >> The mass of a g en critically damped system is released at time t-o rrom the posit on xo = 40 mm with a negative initial velocity. The mass m is 13 kg and the spring constant k is 836 N m. Determine the critical value or the initial velocity Gode below which the mass will pass through the equilibrium position Answer: (to,--371.52 the tolerance is t/296 -371.87 mm/s)
Answer Preview: 371 87 mm s Explanation The critical value of the initial ve…

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, Chapter: 2 -Problem: 87 >> A projectile is launched from point A with the initial conditions shown in the figure. Determine the slant distance s which locates the point B of impact. Calculate the time of flight t. Transcribed Image Text: vo = 120 m/s A e = 40° 20° -800 m Problem 2/87
Answer Preview: Vx v cos 0 VYA 120 cos 40 91 03 m s tB XBXA VxtB …

, Chapter: 5 -Problem: 34 >> The Scotch-yoke mechanism converts rotational motion of the disk to oscillatory translation of the shaft. For given values of ?, ?, ?, r, and d, determine the velocity and acceleration of point P of the shaft. Transcribed Image Text: A r. aY -d-
Answer Preview: velocity and acceleration of any point on shaft is same as it moves in fixed straight line …

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, Chapter: 3 -Problem: 294 >> A spacecraft moving in a west-to-east equatorial orbit is observed by a tracking station located on the equator. If the spacecraft has a perigee altitude H = 150 km and velocity v when directly over the station and an apogee altitude of 1500 km, determine an expression for the angular rate p (relative to the earth) at which the antenna dish must be rotated when the spacecraft is directly overhead.
Answer Preview: The angular rate at which the antenna dish must be rotated when the spacecraft is directly overhead …

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, Chapter: 3 -Problem: 187 >> The tow truck with attached 1200-kg car accelerates uniformly from 30 km/h to 70 km/h over a 15-s interval. The average rolling resistance for the car over this speed interval is 500 N. Assume that the 60° angle shown represents the time average configuration and determine the average tension in the tow cable. Transcribed
Answer Preview: The acceleration of the tow truck and attached car can be c…

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, Chapter: 8 -Problem: 40 >> Derive the equation of motion for the system shown in terms of the displacement x. The masses are coupled through the light connecting rod ABC which pivots about the smooth bearing at point O. Neglect all friction, consider the rollers on m2 and m3 to be light, and assume small oscillations about the equilibrium position. State the system natural circular frequency wn and the viscous damping ratio
Answer Preview: The equation of motion for the system can be derived by applying Newton s Second Law of Motion to ea…

, Chapter: 3 -Problem: 315 >> A ball is released from rest relative to the elevator at a distance h1 above the floor. The speed of the elevator at the time of ball release is v0. Determine the bounce height h2 of the ball (a) If v0 is constant (b) If an upward elevator acceleration a = g/4 begins at the instant the ball is released. The coefficient of restitution for the impact is e.
Answer Preview: a If v0 is constant the bounce height h2 of the bal…

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, Chapter: 3 -Problem: 155 >> The two 1.5-kg spheres are released from rest and gently nudged outward from the position ? = 0 and then rotate in a vertical plane about the fixed centers of their attached gears, thus maintaining the same angle ? for both rods. Determine the velocity v of each sphere as the rods pass the position ? = 30°. The spring is unstretched when ? = 0, and the masses of the two identical rods and the two
Answer Preview: The velocity of each sphere can be determined using the equation o…

, Chapter: 5 -Problem: 8 >> The drive mechanism imparts to the semicircular plate simple harmonic motion of the form ? = ?0 sin ?0t, where ?0 is the amplitude of the oscillation and ?0 is its circular frequency. Determine the amplitudes of the angular velocity and angular acceleration and state where in the motion cycle these maxima occur. Note that this motion is not that of a freely pivoted and undriven body undergoing arb
Answer Preview: The angular velocity of the semicircular plate is given by t…

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, Chapter: 3 -Problem: 283 >> Just after launch from the earth, the space-shuttle orbiter is in the 37 × 137-mi orbit shown. The first time that the orbiter passes the apogee A, its two orbital-maneuvering-system (OMS) engines are fired to circularize the orbit. If the weight of the orbiter is 175,000 lb and the OMS engines have a thrust of 6000 lb each, determine the required time duration ?t of the burn.
Answer Preview: The first step in solving this problem is to calculate the change in velocity v re…

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, Chapter: 3 -Problem: 215 >> Determine the magnitude HO of the angular momentum of the 2-kg sphere about point O (a) By using the vector definition of angular momentum (b) By using an equivalent scalar approach. The center of the sphere lies in the x-y plane. Transcribed Image Text: y 2 kg 30° 9 m/s 5 m 12 m
Answer Preview: H o r mV m 2Kg V 9 cos30i sin330j m s r 12i 5j m H o 2 1…

, Chapter: 5 -Problem: 94 >> Roller B of the quarter-circular link has a velocity vB = 3 ft /sec directed down the 15° incline. The link has a counterclockwise angular velocity w = 2 rad /sec. By the method of this article, determine the velocity of roller A. Transcribed Image Text: A 6" UB 15°
Answer Preview: To determine the velocity of roller A we can use the relative velocity method This method involves c…

, Chapter: 8 -Problem: 36 >> The system shown is released from rest from an initial position x0. Determine the overshoot displacement x1. Assume translational motion in the x-direction. Transcribed Image Text: k = 108 N/m c 18 N.s/m m = 3 kg t X1
Answer Preview: The overshoot displacement x1 can be determined by …

, Chapter: 3 -Problem: 259 >> Sphere A has a mass of 23 kg and a radius of 75 mm, while sphere B has a mass of 4 kg and a radius of 50 mm. If the spheres are traveling initially along the parallel paths with the speeds shown, determine the velocities of the spheres immediately after impact. Specify the angles ?A and ?B with respect to the x-axis made by the rebound velocity vectors. The coefficient of restitution is 0.4 and fr
Answer Preview: lets We can use conservation of momentum and the coefficient of restitution to solve for the velocities of the spheres after impact First let s calcul…

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, Chapter: 3 -Problem: 174 >> The two orbital maneuvering engines of the space shuttle develop 26 kN of thrust each. If the shuttle is traveling in orbit at a speed of 28 000 km/h, how long would it take to reach a speed of 28 100 km/h after the two engines are fi red? The mass of the shuttle is 90 Mg.
Answer Preview: The acceleration of the shuttle can be calculated by di…

, Chapter: 2 -Problem: 157 >> The small block P starts from rest at time t = 0 at point A and moves up the incline with constant acceleration a. Determine r? as a function of time. Transcribed Image Text: of A ? — ? -R- Problem 2/157
Answer Preview: 0 1 2 a at At t 0 u 0 After time t the b…

, Chapter: 5 -Problem: 29 >> Slider A moves in the horizontal slot with a constant speed v for a short interval of motion. Determine the angular velocity ? of bar AB in terms of the displacement xA. Transcribed Image Text: 40° A XA-
Answer Preview: The angular velocity of bar AB can be determined by using the equation v r where v is …

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, Chapter: 3 -Problem: 218 >> The particle of mass m is gently nudged from the equilibrium position A and subsequently slides along the smooth elliptical path which lies in a vertical plane. Determine the magnitude of its angular momentum about point O as it passes (a) point B and (b) point C. In each case, determine the time rate of change of HO. Tran
Answer Preview: a The magnitude of the angular momentum of the particle about point O at po…

, Chapter: 8 -Problem: 126 >> Calculate the damping ratio ? of the system shown if the weight and radius of gyration of the stepped cylinder are W = 20 lb and k? = 5.5 in., the spring constant is k = 15 lb/in., and the damping coefficient of the hydraulic cylinder is c = 2 lb-sec/ft. The cylinder rolls without slipping on the radius r = 6 in. and the spring can support tension as well as compression.
Answer Preview: The damping ratio of the system can be calculated using the following equation c 2mk Where m is the …

, Chapter: 3 -Problem: 160 >> Upon its return voyage from a space mission, the spacecraft has a velocity of 24 000 km /h at point A, which is 7000 km from the center of the earth. Determine the velocity of the spacecraft when it reaches point B, which is 6500 km from the center of the earth. The trajectory between these two points is outside the effect of the earth’s atmosphere.
Answer Preview: The velocity of the spacecraft when it reaches point B can be determined using the equation of conse…

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, Chapter: 4 -Problem: 80 >> At a bulk loading station, gravel leaves the hopper at the rate of 220 lb/sec with a velocity of 10 ft/sec in the direction shown and is deposited on the moving flatbed truck. The tractive force between the driving wheels and the road is 380 lb, which overcomes the 200 lb of frictional road resistance. Determine the acceleration a of the truck 4 seconds after the hopper is opened over the truck be
Answer Preview: Given Rate of gravel …

, Chapter: 9 -Problem: 73 >> Determine the moment of inertia I about axis O-M for the uniform slender rod bent into the shape shown. Plot I versus ? from ? = 0 to ? = 90° and determine the minimum value of I and the angle a which its axis makes with the x-direction. (Note: Because the analysis does not involve the z-coordinate, the expressions developed for area moments of inertia, Eqs. A /9, A /10, and A /11 in Appendix A of
Answer Preview: To determine the moment of inertia about axis O M for the bent rod we need to analyze the rod segmen…

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, Chapter: 2 -Problem: 86 >> A projectile is launched from point O with the initial conditions shown. Determine the impact coordinates for the projectile if (a) v0 = 60 ft/sec and ? = 40° and (b) v0 = 85 ft /sec and ? = 15°. Transcribed Image Text: y | Vo o! -x 40 20 -80' 60'- 100 Problem 2/86
Answer Preview: Solution a For v0 60 ft sec and 40 we can use the following formulas x x0 v0x …

, Chapter: 5 -Problem: 4 >> Magnetic tape is fed over and around the light pulleys mounted in a computer frame. If the speed v of the tape is constant and if the ratio of the magnitudes of the acceleration of points A and B is 2/3, determine the radius r of the larger pulley. Transcribed Image Text: B 3" ?
Answer Preview: The radius of the larger pulley can be determined using the …

, Chapter: 7 -Problem: 99 >> The special-purpose fan is mounted as shown. The motor armature, shaft, and blades have a combined mass of 2.2 kg with radius of gyration of 60 mm. The axial position b of the 0.8-kg block A can be adjusted. With the fan turned off, the unit is balanced about the x-axis when b = 180 mm. The motor and fan operate at 1725 rev/min in the direction shown. Determine the value of b which will produce a
Answer Preview: To determine the value of b which will produce a steady precession of 0 2 rad s about the …

, Chapter: 3 -Problem: 144 >> Determine the unstretched spring length which would cause the 3-lb collar of the previous problem to have no speed as it arrives at position B. All other conditions of the previous problem remain the same.
Answer Preview: The unstretched spring length which would cause th…

, Chapter: 8 -Problem: 45 >> A viscously damped spring-mass system is excited by a harmonic force of constant amplitude F0 but varying frequency w. If the amplitude of the steady-state motion is observed to decrease by a factor of 8 as the frequency ratio w/wn is varied from 1 to 2, determine the damping ratio ? of the system.
Answer Preview: The damping ratio of a system can be determined by examining the amplitude of the st…

, Chapter: 3 -Problem: 202 >> The 2.4-kg particle moves in the horizontal x-y plane and has the velocity shown at time t = 0. If the force F = 2 + 3t2/4 newtons, where t is time in seconds, is applied to the particle in the y-direction beginning at time t = 0, determine the velocity v of the particle 4 seconds after F is applied and specify the corresponding angle ? measured counterclockwise from the x-axis to the direction of
Answer Preview: To determine the velocity of the particle 4 seconds after the force is applied we need to use t…

, Chapter: 2 -Problem: 82 >> An out fielder experiments with two different trajectories for throwing to home plate from the position shown: (a) v0 = 42 m /s with ? = 8° and (b) v0 = 36 m/s with ? = 12°. For each set of initial conditions, determine the time t required for the baseball to reach home plate and the altitude h as the ball crosses the plate.
Answer Preview: For the first set of initial conditions a v0 42 m s with 8 the time t required for the …

, Chapter: 5 -Problem: 27 >> The design characteristics of a gear-reduction unit are under review. Gear B is rotating clockwise with a speed of 300 rev/min when a torque is applied to gear A at time t = 2 s to give gear A a counterclockwise angular acceleration ? which varies with time for a duration of 4 seconds as shown. Determine the speed NB of gear B when t = 6 s.
Answer Preview: The speed of gear B at time t 6 s will be determined by the angular acceleration …

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, Chapter: 3 -Problem: 298 >> At the instant represented in the figure, a small experimental satellite A is ejected from the shuttle orbiter with a velocity vr = 100 m /s relative to the shuttle, directed toward the center of the earth. The shuttle is in a circular orbit of altitude h = 200 km. For the resulting elliptical orbit of the satellite, determine the semimajor axis a and its orientation, the period ?, eccentricity e,
Answer Preview: The semimajor axis of the satellite s orbit can be calculated using the equation a h 1 e where h is the altitude of the shuttle and e is the eccentric…

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, Chapter: 3 -Problem: 196 >> The spring of modulus k = 200 N/m is compressed a distance of 300 mm and suddenly released with the system at rest. Determine the absolute velocities of both masses when the spring is unstretched. Neglect friction. Transcribed Image Text: k = 200 N/m 7 kg 3 kg
Answer Preview: The equation for the spring force is given by F kx where F is the force k is the spring con…

, Chapter: 2 -Problem: 134 >> Motion of the sliding block P in the rotating radial slot is controlled by the power screw as shown. For the instant represented, ?? = 0.1 rad/s, ?¨ = ?0.04 rad /s2, and r = 300 mm. Also, the screw turns at a constant speed giving r? = 40 mm/s. For this instant, determine the magnitudes of the velocity v and acceleration a of P. Sketch v and a if ? = 120°.
Answer Preview: Given 0 1 rad s 0 04 rad s2 r 40 mm s 0 120 For velocity v we have to fin…

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, Chapter: 3 -Problem: 220 >> Just after launch from the earth, the space-shuttle orbiter is in the 37 × 137–mi orbit shown. At the apogee point A, its speed is 17,290 mi/hr. If nothing were done to modify the orbit, what would be its speed at the perigee P? Neglect aerodynamic drag. (Note that the normal practice is to add speed at A, which raises the perigee altitude to a value that is well above the bulk of the atmosphere.)
Answer Preview: To solve this problem we can make use of the principle of conservation of angular momentum In the ab…

, Chapter: 8 -Problem: 86 >> The mechanism shown oscillates in the vertical plane about the pivot O. The springs of equal stiffness k are both compressed in the equilibrium position ? = 0. Determine an expression for the period  ? of small oscillations about O. The mechanism has a mass m with mass center G, and the radius of gyration of the assembly about O is kO.
Answer Preview: To determine the expression for the period of small oscillations we need to analyze the forces acting on the mechanism and apply Newton s second law o…

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, Chapter: 8 -Problem: 26 >> The period ?d of damped linear oscillation for a certain 1-kg mass is 0.3 s. If the stiffness of the supporting linear spring is 800 N/m, calculate the damping coefficient c.
Answer Preview: c 160 Ns m Explanation The damping coe…

, Chapter: 3 -Problem: 230 >> The particle of mass m is launched from point O with a horizontal velocity u at time t = 0. Determine its angular momentum HO relative to point O as a function of time. Transcribed Image Text: m y L--x
Answer Preview: The angular momentum HO of the particle relative to point O can be determined by using the equation …

, Chapter: 9 -Problem: 28 >> Determine the mass moment of inertia and corresponding radius of gyration of the thin homogeneous parabolic shell about the y-axis. The shell has dimensions r = 70 mm and h = 200 mm, and is made of metal plate having a mass per unit area of 32 kg/m2. Transcribed Image Text: h
Answer Preview: The mass moment of inertia of a thin homogeneous parabolic shell about the …

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, Chapter: 3 -Problem: 263 >> The 3000-kg anvil A of the drop forge is mounted on a nest of heavy coil springs having a combined stiffness of 2.8(106) N/m. The 600-kg hammer B falls 500 mm from rest and strikes the anvil, which suffers a maximum downward deflection of 24 mm from its equilibrium position. Determine the height h of rebound of the hammer and the coefficient of restitution e which applies.
Answer Preview: To determine the height of rebound of the hammer and the coefficient of restitution we need to use t…

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, Chapter: 2 -Problem: 99 >> The car moves on a horizontal surface without any slippage of its tires. For each of the eight horizontal acceleration vectors, describe in words the instantaneous motion of the car. The car velocity is directed to the left as shown for all cases. Transcribed Image Text: az a2. a5 a6 as Problem 2/99
Answer Preview: Case 1 The car is accelerating to the left Case 2 The car is maintaining it…

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, Chapter: 3 -Problem: 232 >> A particle of mass m is released from rest in position A and then slides down the smooth vertical-plane track. Determine its angular momentum about both points A and D (a) As it passes position B (b) As it passes position C. Transcribed Image Text: D m A 30° B C
Answer Preview: A a 30 V Vd 2gp sin30 Vb 2g p sin 30 Vc 2gpsin30 …

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, Chapter: 2 -Problem: 108 >> A particle moves along the curved path shown. If the particle has a speed of 40 ft/sec at A at time tA and a speed of 44 ft/sec at B at time tB, determine the average values of the acceleration of the particle between A and B, both normal and tangent to the path. Transcribed Image Text: B 26° tg = 3
Answer Preview: The following are given by th…

, Chapter: 3 -Problem: 253 >> A small ball is projected horizontally toward an incline as shown. Determine the slant range R. The initial speed is v0 = 16 m /s, and the coefficient of restitution for the impact at A is e = 0.6. Transcribed Image Text: R' vo A 40°
Answer Preview: g X V Vy Q 400 Vx V Cose Vx 16 Cos 40 12 26 V e V sine Vy 0 6 x 16 x sin 40 …

, Chapter: 8 -Problem: 67 >> Derive and solve the equation of motion for the mass m in terms of the variable x for the system shown. Neglect the mass of the lever AOC and assume small oscillations. Transcribed Image Text: C k2 k1 ww ? TxB = bo cos ot A a
Answer Preview: The equation of motion for the mass m in terms of the variable x can be derived using Newton …

, Chapter: 2 -Problem: 239 >> The launching catapult of the aircraft carrier gives the jet fighter a constant acceleration of 50 m/s2 from rest relative to the flight deck and launches the aircraft in a distance of 100 m measured along the angled takeoff ramp. If the carrier is moving at a steady 30 knots (1 knot = 1.852 km/h), determine the magnitude v of the actual velocity of the fighter when it is launched.
Answer Preview: The magnitude v of the actual velocity of the fighter when it is launched can be determined by using …

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, Chapter: 3 -Problem: 278 >> A “drag-free” satellite is one which carries a small mass inside a chamber as shown. If the satellite speed decreases because of drag, the mass speed will not, and so the mass moves relative to the chamber as indicated. Sensors detect this change in the position of the mass within the chamber, and the satellite thruster is periodically fired to re-center the mass. In this manner, compensation is m
Answer Preview: The drag force D acting on the 100 kg satellite can b…

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, Chapter: 2 -Problem: 245 >> Cylinder A has a constant downward speed of 1 m/s. Compute the velocity of cylinder B for (a) ? = 45°, (b) ? = 30°, and (c) ? = 15°. The spring is in tension throughout the motion range of interest, and the pulleys are connected by the cable of fixed length. Transcribed Image Text: A 1 m/s B Problem
Answer Preview: For a 45 The velocity of cylinder B can be calculated using the equation vB vA cos Therefore …

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, Chapter: 3 -Problem: 289 >> Determine the necessary amount ?v by which the circular-orbit velocity of satellite C should be reduced if the catch-up maneuver of Prob. 3/288 is to be accomplished with not one but two periods in a new elliptical orbit.
Answer Preview: In order to determine the necessary amount of v by which the circular orbit velocity of satellite C …

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, Chapter: 2 -Problem: 190 >> For the instant represented, car A has an acceleration in the direction of its motion, and car B has a speed of 45 mi/hr which is increasing. If the acceleration of B as observed from A is zero for this instant, determine the acceleration of A and the rate at which the speed of B is changing. Transcribed Image Text:
Answer Preview: From the data given The radius of the car R 600 ft Velocity of the car B V B 45 mi hrV B 45mi hr We …

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, Chapter: 2 -Problem: 222 >> The hoisting system shown is used to easily raise kayaks for overhead storage. Determine expressions for the upward velocity and acceleration of the kayak at any height y if the winch M reels in cable at a constant rate l?. Assume that the kayak remains level. Transcribed Image Text: -- y M A B b- P
Answer Preview: We can start by analyzing the forces acting on the kayak at any height y Since the kayak remains lev…

, Chapter: 2 -Problem: 83 >> A ski jumper has the takeoff conditions shown. Determine the inclined distance d from the takeoff point A to the location where the skier first touches down in the landing zone, and the total time tƒ during which the skier is in the air. For simplicity, assume that the landing zone BC is straight. Transcribed Image Text:
Answer Preview: Horizontal distance travelled by the skier x vo coset t x cos Vertical distance travelled by the ski…

, Chapter: 4 -Problem: 82 >> A coil of heavy flexible cable with a total length of 100 m and a mass of 1.2 kg/m is to be laid along a straight horizontal line. The end is secured to a post at A, and the cable peels off the coil and emerges through the horizontal opening in the cart as shown. The cart and drum together have a mass of 40 kg. If the cart is moving to the right with a velocity of 2 m/s when 30 m of cable remain i
Answer Preview: The force P required to give the cart and drum an …

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, Chapter: 2 -Problem: 162 >> At time t = 0, the baseball player releases a ball with the initial conditions shown in the figure. Determine the quantities r, r?, r¨, ?, ??, and ?¨, all relative to the x-y coordinate system shown, at time t = 0.5 sec. Transcribed Image Text: y vo = 100 ft/sec a = 30° 6' Problem 2/162
Answer Preview: Solution From the figure r 7 ft From the initial conditions r 0 8 ft Therefore distance travele…

, Chapter: 2 -Problem: 119 >> A spacecraft S is orbiting Jupiter in a circular path 1000 km above the surface with a constant speed. Using the gravitational law, calculate the magnitude v of its orbital velocity with respect to Jupiter. Use Table D /2 of Appendix D as needed. Transcribed Image Text: 1000 km Problem 2/119
Answer Preview: To calculate the magnitude v of the orbital velocity of the spacecraft S with r…

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, Chapter: 9 -Problem: 10 >> Determine the mass moment of inertia of the homogeneous solid of revolution of the previous problem about the y- and z-axes.
Answer Preview: The mass moment of inertia for a solid of revolution …

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, Chapter: 2 -Problem: 112 >> A minivan starts from rest on the road whose constant radius of curvature is 40 m and whose bank angle is 10°. The motion occurs in a horizontal plane. If the constant forward acceleration of the minivan is 1.8 m/s2, determine the magnitude a of its total acceleration 5 seconds after starting.

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