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Chapter: 12 -Problem: 48 >> The s–t graph for a train has been determined experimentally. From the data, construct the v–t and a–t graphs for the motion. Transcribed Image Text: s (m) 600 360 s 24t360- s = 0.41² 30 40 Hote -t (s)
Answer Preview: vt Graph The velocity in terms of time t can be obtained by applying v …

, Chapter: 22 -Problem: 62 >> The motor of mass M is supported by a simply supported beam of negligible mass. If block A of mass m is clipped onto the rotor, which is turning at constant angular velocity of , determine the amplitude of the steady-state vibration. When the beam is subjected to a concentrated force of P at its mid-span, it deflects ? = PL3/48EI at this point. Here E is Young’s modulus of elasticity, a property o
Answer Preview: In this case Thus the na…

, Chapter: 16 -Problem: 75 >> Piston P moves upward with a velocity of 300in./s at the instant shown. Determine the angular velocity of the crankshaft AB at this instant. Transcribed Image Text: Up = 300 in./s ? G- 30° P B. 5 in. 2.75 in. 1.45 in.
Answer Preview: From the geometry For link BP Equ…

, Chapter: 15 -Problem: 112 >> The 2-kg ball rotates around a 0.5-m-diameter circular path with a constant speed. If the cord length is shortened from 1 = 1 m to ?' = 0.5 m, by pulling the cord through the tube, determine the new diameter of the path d'. Also, what is the tension in the cord in each case? Transcribed Image Text:
Answer Preview: Equation of Motion When the ball is travelling around the 0 5 m diameter circular path App…

, Chapter: 9 -Problem: 22 >> Locate the centroid y? of the area. Transcribed Image Text: 16 ft -y = (4-x²)² 4 ft- T 4 ft +
Answer Preview: Area and Moment Arm The area of t…

, Chapter: 17 -Problem: 102 >> The slender, 200-kg beam is suspended by a cable at its end as shown. If a man pushes on its other end with a horizontal force of 30 N, determine the initial acceleration of its mass center G, the beam’s angular acceleration, the tension in the cable AB, and the initial acceleration of the end A. Transcribed Image Text:
Answer Preview: Equations of Motion At the instant the force F is applied …

, Chapter: 12 -Problem: 50 >> From experimental data, the motion of a jet plane while traveling along a runway is defined by the v–t graph shown. Construct the s–t and a–t graphs for the motion. Transcribed Image Text: v (m/s) 80 10 40 -t (s)
Answer Preview: From the vt …

, Chapter: 22 -Problem: 59 >> Determine the angular velocity of the flywheel in Prob. 22–57 which will produce an amplitude of vibration of 0.25 in. Prob. 22–57The electric motor turns an eccentric flywheel which is equivalent to an unbalanced 0.25-lb weight located 10 in. from the axis of rotation. If the static deflection of the beam is 1 in. because of the weight of the motor, determine the angular velocity of the flywheel
Answer Preview: The constant value F O of the periodic force is due to …

, Chapter: 16 -Problem: 24 >> A pendulum has a swinging motion such that ? = [ - 0.101 sin(4.95t) + 0.3 cos(4.95t) ] rad, where t is in seconds, and the arguments for the sine and cosine are in radians. Determine the magnitudes of the velocity and acceleration of the bob when ? = 0°. Transcribed Image Text: 0.4 m 0
Answer Preview: At t 0 2517 s At t 0 2517 s 0 0 …

, Chapter: 15 -Problem: 81 >> The girl throws the 0.5-kg ball toward the wall with an initial velocity vA = 10 m/s. Determine (a) The velocity at which it strikes the wall at B, (b) The velocity at which it rebounds from the wall if the coefficient of restitution e = 0.5, and (c) The distance s from the wall to where it strikes the ground at C. Transcr
Answer Preview: a b c Kinematics By considering the horizontal motion of the ball …

, Chapter: 9 -Problem: 60 >> Locate the centroid y? for the beam’s cross-sectional area. Transcribed Image Text: 120 mm 240 mm -120 mm X
Answer Preview: 2 2 12024 120 240 600 1…

, Chapter: 17 -Problem: 103 >> The spool has a mass of 75 kg and a radius of gyration kG = 0.380 m. It rests on the inclined surface for which the coefficient of kinetic friction is ?k = 0.15. If the spool is released from rest and slips at A, determine the initial tension in the cord and the angular acceleration of the spool. Transcribed Image Text:
Answer Preview: Solving FA 0 15N A 0 3 …

, Chapter: 12 -Problem: 82 >> The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = c sin kt, y = c cos kt, z = h ? bt, where c, h, and b are constants. Determine the magnitudes of its velocity and acceleration. Transcribed Image Text: ? 2 - ?
Answer Preview: x c sin kt x ck cos kt y c c…

, Chapter: 21 -Problem: 33 >> The 20-kg sphere rotates about the axle with a constant angular velocity of ?s = 60 rad/s. If shaft AB is subjected to a torque of M = 50 N · m, causing it to rotate, determine the value of ?? after the shaft has turned 90° from the position shown. Initially, ?? = 0. Neglect the mass of arm CDE. Transcribed Image Text:
Answer Preview: The mass moments of inertia of the sphere about the x y and z axes are When …

, Chapter: 16 -Problem: 5 >> The disk is driven by a motor such that the angular position of the disk is defined by ? = (20t + 4t2) rad where t is in seconds. Determine the number of revolutions, the angular velocity, and angular acceleration of the disk when t = 90 s. Transcribed Image Text: 0.5 ft
Answer Preview: Angular Displacement At t 90 s A…

, Chapter: 12 -Problem: 113 >> The position of a particle is defined by r = {4(t - sin t)i + (2t2 - 3)j} m, where t is in seconds and the argument for the sine is in radians. Determine the speed of the particle and its normal and tangential components of acceleration when t = 1 s.
Answer Preview: r 4 tsin t i 2t 3 j V 0 dr dt v 1 1 1 83879i 4j V V 1 8387…

, Chapter: 9 -Problem: 114 >> Determine the weight of the wedge which is formed by rotating a right triangle of base 6 in. and height 3 in. through an angle of 30°. The specific weight of the material is ? = 0.22 lb/in3. Transcribed Image Text: 6 in. 30° 3 in.
Answer Preview: y 3 m By symmetry P 240 x 1 FR 6 pdx 5 p d…

, Chapter: 15 -Problem: 1 >> The 0.5-kg ball strikes the rough ground and rebounds with the velocities shown. Determine the magnitude of the impulse the ground exerts on the ball. Assume that the ball does not slip when it strikes the ground, and neglect the size of the ball and the impulse produced by the weight of the ball. Transcribed Image Text:
Answer Preview: The impulse that the ground exerts on the ball can be calculated as the difference in momentum of th…

, Chapter: 12 -Problem: 80 >> The motorcycle travels with constant speed v0 along the path that, for a short distance, takes the form of a sine curve. Determine the x and y components of its velocity at any instant on the curve. Transcribed Image Text: y C -L- - y = c sin (7x) -L C X
Answer Preview: y csin x y 7 c cos Zx x …

, Chapter: 22 -Problem: 40 >> If the wheel is given a small angular displacement of ? and released from rest, it is observed that it oscillates with a natural period of ?. Determine the wheel’s radius of gyration about its center of mass G. The wheel has a mass of m and rolls on the rails without slipping. Transcribed Image Text:
Answer Preview: Potential and Kinetic Energy With reference to the datum es…

, Chapter: 16 -Problem: 13 >> Determine the angular velocity of the rod and the velocity of point C at the instant shown. Transcribed Image Text: 4 m A VA = 6 m/s 2.5 m 2.5 m B
Answer Preview: Given a rod with a length of h with point A moving at a velocity of VA and point C located at a dis…

, Chapter: 12 -Problem: 191 >> The arm of the robot move s so that r = 3 ft is constant, and its grip A moves along the path z = (3 sin 4?) ft, where u is in radians. If ? = (0.5 t) rad, where t is in seconds, determine the magnitudes of the grip’s velocity and acceleration when t = 3 s. Transcribed Image Text: Z A
Answer Preview: 0 0 5 t 0 0 5 0 0 Att 3 s z 0 8382 5 761 …

, Chapter: 10 -Problem: 1 >> Determine the moment of inertia for the area about the x axis. Transcribed Image Text: y y=/r²_ 4 in. 2 in. X
Answer Preview: To determine the moment of inertia for the area about the x axis we can use the f…

, Chapter: 17 -Problem: 112 >> The circular concrete culvert rolls with an angular velocity of ? = 0.5 rad/s when the man is at the position shown. At this instant the center of gravity of the culvert and the man is located at point G, and the radius of gyration about G is kG = 3.5 ft. Determine the angular acceleration of the culvert. The combined weight of the culvert and the man is 500 lb. Assume that the culvert rolls witho
Answer Preview: Equations of Motion The mass moment of inertia of the system about its m…

, Chapter: 12 -Problem: 69 >> If the velocity of a particle is defined as v(t) = {0.8t2i + 12t1/2j + 5k} m/s, determine the magnitude and coordinate direction angles ?, ?, ? of the particle’s acceleration when t = 2 s.
Answer Preview: v t 0 8t i 12t 2 j 5k dv dt Whe…

, Chapter: 21 -Problem: 45 >> The 40-kg flywheel (disk) is mounted 20 mm off its true center at G. If the shaft is rotating at a constant speed ? = 8 rad/s, determine the maximum reactions exerted on the journal bearings at A and B. Transcribed Image Text: 0.75 m 1.25 m 20 mm 500 mm w = 8 rad/s B
Answer Preview: Solving Thus Wx 0 8 r…

, Chapter: 16 -Problem: 51 >> The bar remains in contact with the floor and with point A. If point B moves to the right with a constant velocity vB, determine the angular velocity and angular acceleration of the bar as a function of x. Transcribed Image Text: 0 7. B VB
Answer Preview: Position C…

, Chapter: 12 -Problem: 94 >> A golf ball is struck with a velocity of 80 ft/s as shown. Determine the speed at which it strikes the ground at B and the time of flight from A to B. Transcribed Image Text: VA = 80 ft/s 45° 10? -d- B
Answer Preview: VA x 80 cos 55 44 886 VA y S So vot d cos 10 0 …

, Chapter: 10 -Problem: 15 >> Determine the moment of inertia for the area about the x axis. Transcribed Image Text: y T 4 in. y² = x 16 in. X
Answer Preview: Differential Element The area of the different…

, Chapter: 17 -Problem: 89 >> The “Catherine wheel” is a firework that consists of a coiled tube of powder which is pinned at its center. If the powder burns at a constant rate of 20 g/s such that the exhaust gases always exert a force having a constant magnitude of 0.3 N, directed tangent to the wheel, determine the angular velocity of the wheel when 75% of the mass is burned off. Initially, the wheel is at rest and has a mas
Answer Preview: Mass of wheel when 75 of the powder i…

, Chapter: 12 -Problem: 73 >> The water sprinkler, positioned at the base of a hill, releases a stream of water with a velocity of 15 ft/s as shown. Determine the point B(x, y) where the water strikes the ground on the hill. Assume that the hill is defined by the equation y = (0.05x2) ft and neglect the size of the sprinkler. Transcribed Image Text:
Answer Preview: Since y 0 05x 2 Also Since y 0 05x 2 12 …

, Chapter: 22 -Problem: 61 >> Determine the amplitude of vibration of the trailer in Prob. 22-60 if the speed v = 15 km/h. Prob. 22-60The 450-kg trailer is pulled with a constant speed over the surface of a bumpy road, which may be approximated by a cosine curve having an amplitude of 50 mm and wave length of 4 m. If the two springs s which support the trailer each have a stiffness of 800 N/m, determine the speed which will ca
Answer Preview: As shown in Prob 2250 the velocity is inv…

, Chapter: 16 -Problem: 7 >> The disk is moving to the left such that it has an angular acceleration ? = 8 rad/s² and angular velocity ? = 3 rad/s at the instant shown. If it does not slip at A, determine the acceleration of point B. Transcribed Image Text: B 30° 0.5 m A C w = 3 rad/s a = 8 rad/s²
Answer Preview: The acceleration of point B can be determined using the equation of tangential a…

, Chapter: 12 -Problem: 189 >> A particle moves along an Archimedean spiral r = (80) ft, where is in radians. If ?? = 4 rad/s (constant), determine the radial and transverse components of the particle's velocity and acceleration at the instant = ?/2 rad. Sketch the curve and show the components on the curve. Transcribed Image Text:
Answer Preview: Time Derivatives Since is cons…

, Chapter: 9 -Problem: 100 >> Determine the approximate outer surface area of the funnel. It consists of a full circular part of negligible thickness. Transcribed Image Text: 30 mm 60 mm 50 mm 80 mm 130 mm
Answer Preview: A 0r L 27 …

, Chapter: 15 -Problem: 13 >> Determine the coefficient of restitution e between ball A and ball B. The velocities of A and B before and after the collision are shown. Transcribed Image Text: 8 m/s A Before collision 1 m/s A After collision 2 m/s 9 m/s B B
Answer Preview: Determine the coefficient of restit…

, Chapter: 12 -Problem: 85 >> The flight path of the helicopter as it takes off from A is defined by the parametric equations x = (2t²) m and y = (0.04t³) m, where t is the time in seconds. Determine the distance the helicopter is from point A and the magnitudes of its velocity and acceleration when t = 10 s. Transcribed Image Text:
Answer Preview: x 2 x 200 m d 200 40 204 m Att …

, Chapter: 22 -Problem: 43 >> A 4-lb weight is attached to a spring having a stiffness k = 10 lb/ft. The weight is drawn downward a distance of 4 in. and released from rest. If the support moves with a vertical displacement ? = (0.5 sin 4t) in., where t is in seconds, determine the equation which describes the position of the weight as a function of time.
Answer Preview: The initial condition when …

, Chapter: 16 -Problem: 4 >> The disk is originally rotating at ?0 = 8 rad/s. If it is subjected to a constant angular acceleration of ? = 6 rad/s2, determine the magnitudes of the velocity and the n and t components of acceleration of point B just after the wheel undergoes 2 revolutions. Transcribed Image Text: B 1.5 ft w = 8
Answer Preview: w w 2a 0 0 w 8 2 6 2 2T …

, Chapter: 12 -Problem: 162 >> If a particle’s position is described by the polar coordinates r = (2 sin 2?) m and ? = (4t) rad, where t is in seconds, determine the radial and transverse components of its velocity and acceleration when t = 1 s.
Answer Preview: When t 1 s 0 4t 4 4 0 0 r 2 sin 20 1 9787 …

, Chapter: 9 -Problem: 9 >> Locate the centroid x? of the area. Transcribed Image Text: 4m (y=4x -4m
Answer Preview: Area and Moment Arm The area of t…

, Chapter: 15 -Problem: 42 >> The 5-kg spring-loaded gun rests on the smooth surface. It fires a ball having a mass of 1 kg with a velocity of v' = 6 m/s relative to the gun in the direction shown. If the gun is originally at rest, determine the distance the ball is from the initial position of the gun at the instant the ball reaches its highest elevation C. Neglect the size of the gun.
Answer Preview: So that Time of flight for the ball Horizonta…

, Chapter: 12 -Problem: 23 >> Determine the speed at which the basketball at A must be thrown at the angle of 30° so that it makes it to the basket at B. Transcribed Image Text: 30° -X 1.5 m -10 m- B 3m
Answer Preview: To determine the speed at which the basketball must be thrown we need to calculate the initial veloc…

, Chapter: 22 -Problem: 47 >> If the dashpot has a damping coefficient of c = 50 N · s/m, and the spring has a stiffness of k = 600 N/m, show that the system is underdamped, and then find the pendulum's period of oscillation. The uniform rods have a mass per unit length of 10 kg/m. Transcribed Image Text: A -0.3 m c = 50 N-s/m C
Answer Preview: Equation of Motion When the pendulum rotates point C through a small …

, Chapter: 15 -Problem: 80 >> A ball of negligible size and mass m is given a velocity of v0 on the center of the cart which has a mass M and is originally at rest. If the coefficient of restitution between the ball and walls A and B is e, determine the velocity of the ball and the cart just after the ball strikes A. Also, determine the total time needed for the ball to strike A, rebound, then strike B, and rebound and then re
Answer Preview: After the first collision The relative velocity on the cart …

, Chapter: 12 -Problem: 152 >> A particle P travels along an elliptical spiral path such that its position vector ris defined by {2 cos(0.1t)i + 1.5 sin(0.1t)j + (2t)k} m, where t is in seconds and the arguments for the sine and cosine are given in radians. When t = 8 s, determine the coordinate direction angles ?, ß, and ?, which the binormal axis to the osculating plane makes with the x, y, and z axes. Solve for the velocity
Answer Preview: When t 8 s Since the binormal vector is perpendicular to the plane containing the n…

, Chapter: 9 -Problem: 53 >> Determine the location y? of the centroid C of the “rollformed” member. Neglect the thickness of the material and any slight bends at the corners. Transcribed Image Text: 40 mm y C 20 mm 40 mm 150 mm X
Answer Preview: L 2 20 150 150 …

, Chapter: 17 -Problem: 88 >> The 4-kg slender rod is initially supported horizontally by a spring at B and pin at A. Determine the angular acceleration of the rod and the acceleration of the rod’s mass center at the instant the 100-N force is applied. Transcribed Image Text: A -1.5 m- 100 N -1.5 m- B k = 20 N/m
Answer Preview: Equation of Motion The mass moment of inertia of the rod about A i…

, Chapter: 12 -Problem: 32 >> The car travels up the hill with a speed of v = (0.2s) m/s, where s is in meters, measured from A. Determine the magnitude of its acceleration when it is at s = 50 m, where ? = 500 m. Transcribed Image Text: A s = 50 m- n -X
Answer Preview: The magnitude of the acceleration of the car can be determined using the f…

, Chapter: 21 -Problem: 15 >> Determine the moment of inertia of both the 1.5-kg rod and 4-kg disk about the z? axis. Transcribed Image Text: 300 mm -100 mm.
Answer Preview: Due to symmetry I xy I yz I zx 0 Iy I x 1 4 0 1 …

, Chapter: 15 -Problem: 45 >> The block of mass m travels at v? in the direction ?? shown at the top of the smooth slope. Determine its speed v? and its direction ?2 when it reaches the bottom. Transcribed Image Text: h X N 20? 202
Answer Preview: There are no impulses in the …

, Chapter: 12 -Problem: 187 >> If the cam rotates clockwise with a constant angular velocity of ?? = 5 rad/s, determine the magnitudes of the velocity and acceleration of the follower rod AB at the instant ? = 30°. The surface of the cam has a shape of limaçon defined by r = (200 + 100 cos ?) mm. Transcribed Image Text: r = (200
Answer Preview: Time Derivatives When …

, Chapter: 5 -Problem: 80 >> The bent rod is supported at A, B, and C by journal bearings. Determine the components of reaction at bearings if the rod is subjected to the 200-lb vertical force and the 30 lb-ft couple moment. The bearings are in proper alignment and exert only force reactions on the rod. Transcribed Image Text:
Answer Preview: Solving Eqs 1 to 6 yields Negative signs in…

, Chapter: 15 -Problem: 12 >> The cannon and support without a projectile have a mass of 250 kg. If a 20-kg projectile is fired from the cannon with a velocity of 400 m/s, measured relative to the cannon, determine the speed of the projectile as it leaves the cannon barrel. Neglect rolling resistance. Transcribed Image Text: 30°
Answer Preview: 400 m s Explain The speed of the projectile as it leaves the cannon barrel is equal to th…

, Chapter: 12 -Problem: 20 >> The box slides down the path described by the equation y = (0.05x²) m, where x is in meters. If the box has x components of velocity and acceleration of vx, = -3 m/s and ax = -1.5 m/s² at x = 5 m, determine the y components of the velocity and the acceleration of the box at this instant. Transcribed Image Text:
Answer Preview: Given that the path of the box is described by the equation y 0 05x 2 m a…

, Chapter: 22 -Problem: 41 >> If the block-and-spring model is subjected to the periodic force F = F0cos ot, show that the differential equation of motion is x? + (k/m)x= (F0/m) cos ?t, where x is measured from the equilibrium position of the block. What is the general solution of this equation? Transcribed Image Text: Equilibri
Answer Preview: The general solution of the above differential equation is of the form of …

, Chapter: 15 -Problem: 104 >> At the instant r = 1.5 m, the 5-kg disk is given a speed of v = 5 m/s, perpendicular to the elastic cord. Determine the speed of the disk and the rate of shortening of the elastic cord at the instant r = 1.2 m. The disk slides on the smooth horizontal plane. Neglect its size. The cord has an unstretched length of 0.5 m. Tr
Answer Preview: Conservation of Energy The intial and final stretch of the elastic cord is s 1 1 5 0 …

, Chapter: 12 -Problem: 161 >> If a particle moves along a path such that r = (2 cost) ft and ? = (t/2) rad, where t is in seconds, plot the path r = f(?) and determine the particle's radial and transverse components of velocity and acceleration.
Answer Preview: t 20 r 2 cost r 2 sin t 0 7 7 2 r 2 cos …

, Chapter: 9 -Problem: 29 >> Locate the centroid y? of the area. Transcribed Image Text: y 100 mm -100 mm- y = x = 100 X
Answer Preview: Area and Moment Arm Here x 10y 2 and x y Thus the area of …

, Chapter: 17 -Problem: 97 >> The spool has a mass of 100 kg and radius of gyration about its mass center of kG = 0.3 m. Determine the smallest coefficient of static friction that will prevent slipping on the rail at A. What is the angular acceleration of the spool? Transcribed Image Text: 0.5 m 0.25 m A G 250 N
Answer Preview: Equations of Motion The mass moment of inertia of the spool about its center of …

, Chapter: 17 -Problem: 9 >> Determine the moment of inertia Iz of the frustum of the cone, which has a conical depression. The material has a density of 200 kg/m3. Transcribed Image Text: 200 mm- 800 mm Z 600 mm 400 mm
Answer Preview: From similar tri…

, Chapter: 12 -Problem: 34 >> The platform is rotating about the vertical axis such that at any instant its angular position is = (4/³/2) rad, where t is in seconds. A ball rolls outward along the radial groove so that its position is r = (0.1t³) m, where t is in seconds. Determine the magnitudes of the velocity and acceleration of the ball when t = 1.5 s.
Answer Preview: The velocity of the ball at any time t can be calculated by taking the derivative of the p…

, Chapter: 21 -Problem: 34 >> The 25-lb thin plate is suspended from a ball-and-socket joint at O. A 0.2-lb projectile is fired with a velocity of v = {-300i - 250j + 300k} ft/s into the plate and becomes embedded in the plate at point A. Determine the angular velocity of the plate just after impact and the axis about which it begins to rotate. Neglect the mass of the projectile after it embeds into the plate.
Answer Preview: Angular momentum about point O is conserved Axis of rotation line is along Ho Ho TOAX mp p 0 …

, Chapter: 15 -Problem: 55 >> A box A, having a mass of 20 kg, is released from rest at the position shown and slides freely down the smooth inclined ramp. When it reaches the bottom of the ramp, it slides horizontally onto the surface of a 10-kg cart for which the coefficient of kinetic friction between the cart and the box is ?k = 0.6. If h = 0.2 m, determine the final velocity of the cart once the block comes to rest on it.
Answer Preview: Conservation of Energy Conservation of Moment…

, Chapter: 12 -Problem: 168 >> A particle travels along the portion of the "four-leaf rose" defined by the equation r = (5 cos 2?) m. If the angular velocity of the radial coordinate line is ? = (3t²) rad/s, where t is in seconds, determine the radial and transverse components of the particle's velocity and acceleration at the instant = 30°. When t = 0, ? = 0.
Answer Preview: 0 31 0 6t do 3 dr dt 0 t At 0 0 t 6 3 0 806 0 r 3…

, Chapter: 10 -Problem: 4 >> Determine the moment of inertia of the triangular area about the y axis. Transcribed Image Text: h ?y = (b ? x) -b- -X
Answer Preview: Area of the diff…

, Chapter: 17 -Problem: 101 >> If the coefficient of static friction at C is ?s = 0.3, determine the largest force F that can be applied to the 5-kg ring without causing it to slip. Neglect the thickness of the ring. Transcribed Image Text: G 0.4 m C 30° A 45° F
Answer Preview: Equations of Motion The mass moment of inertia of the ring about its center of gravity …

, Chapter: 17 -Problem: 7 >> Determine the moment of inertia of the semi ellipsoid with respect to the x axis and express the result in terms of the mass m of the semi ellipsoid. The material has a constant density ?. Transcribed Image Text: + 1 b X
Answer Preview: Thus dIx ydm 2 …

, Chapter: 12 -Problem: 40 >> An airplane starts from rest, travels 5000 ft down a runway, and after uniform acceleration, takes off with a speed of 162 mi/h. It then climbs in a straight line with a uniform acceleration of 3 ft/s² until it reaches a constant speed of 220 mi/h. Draw the s-t, v-t, and a-t graphs that describe the motion.
Answer Preview: 2 0 mi 1h 5280 ft h 3600 s 1 mi 22 162 v v 2a s S1 237 6 0 2 a 5000 0 …

, Chapter: 22 -Problem: 67 >> A block having a mass of 7 kg is suspended from a spring that has a stiffness k = 600 N/m. If the block is given an upward velocity of 0.6 m/s from its equilibrium position at t = 0, determine its position as a function of time. Assume that positive displacement of the block is downward and that motion takes place in a medium which furnishes a damping force F = (50|v|) N, where v is in m/s.
Answer Preview: Since c c z the system is underdamped …

, Chapter: 15 -Problem: 50 >> Using the data in Prob. 15–49, determine the distance the crate slides on the barge before coming to rest. Prob. 15–49The crate has a mass m and rests on the barge which has a mass M and is initially at rest. The coefficient of kinetic friction between the crate and barge is ?. The rope is pulled (or jerked) such that it snaps and as a result the impulse gives the barge a sudden velocity v0. Deter
Answer Preview: Crate Barge Integrat…

, Chapter: 12 -Problem: 163 >> The driver of the car maintains a constant speed of 40 m/s. Determine the angular velocity of the camera tracking the car when ? = 15°. Transcribed Image Text: r = (100 cos 20) m, OJ
Answer Preview: Time Derivatives Velocity Referring t…

, Chapter: 9 -Problem: 26 >> Locate the centroid x? of the area. Transcribed Image Text: 4 ft y 4 ft X
Answer Preview: Area and Moment Arm The area of …

, Chapter: 17 -Problem: 117 >> The uniform beam has a weight W. If it is originally at rest while being supported at A and B by cables, determine the tension in cable A if cable B suddenly fails. Assume the beam is a slender rod. Transcribed Image Text: L A A ? B -?-
Answer Preview: Since Also Sin…

, Chapter: 17 -Problem: 69 >> The passengers, the gondola, and its swing frame have a total mass of 50 Mg, a mass center at G, and a radius of gyration kB = 3.5 m. Additionally, the 3-Mg steel block at A can be considered as a point of concentrated mass. Determine the horizontal and vertical components of reaction at pin B if the gondola swings freely at ? = 1 rad/s when it reaches its lowest point as shown. Also, what is the
Answer Preview: Equations of Motion The mass moment of inertia of the gondola and the counter wei…

, Chapter: 12 -Problem: 28 >> A train is initially traveling along a straight track at a speed of 90 km/h. For 6 s it is subjected to a constant deceleration of 0.5 m/s2, and then for the next 5 s it has a constant deceleration ac. Determine ac so that the train stops at the end of the 11-s time period.
Answer Preview: First stage of …

, Chapter: 22 -Problem: 76 >> Determine the differential equation of motion for the damped vibratory system shown. What type of motion occurs? Take k = 100 N/m, c = 200 N · s/m,m = 25 kg. Transcribed Image Text: C et C www.c
Answer Preview: Free body Diagram When the block is being displaced by an amount y vertically downward the r…

, Chapter: 15 -Problem: 106 >> The two spheres A and B each have a mass of 400 g. The spheres are fixed to the horizontal rods and their initial velocity is 2 m/s. If a couple moment of M = 0.6 N · m is applied to the frame, determine the speed of the spheres in 3 s. The mass of the supporting frame is negligible and it is free to rotate. Neglect the size of the spheres.
Answer Preview: Principle of Angula…

, Chapter: 12 -Problem: 107 >> The firefighter wishes to direct the flow of water from his hose to the fire at B. Determine two possible angles ?? and ?2 at which this can be done. Water flows from the hose at vA = 80 ft/s. Transcribed Image Text: 0 -35 ft B 20 ft
Answer Preview: Thus Solving 1 …

, Chapter: 9 -Problem: 20 >> Determine the magnitude of the hydrostatic force acting on gate AB, which has a width of 2 m. Water has a density of ? = 1 Mg/m³. Transcribed Image Text: 3 m 2 m A B
Answer Preview: The magnitude of the hydrostatic force can be calculated using …

, Chapter: 17 -Problem: 77 >> Disk D turns with a constant clockwise angular velocity of 30 rad/s. Disk E has a weight of 60 lb and is initially at rest when it is brought into contact with D. Determine the time required for disk E to attain the same angular velocity as disk D. The coefficient of kinetic friction between the two disks is ?k = 0.3. Neglect the weight of bar BC.
Answer Preview: Equations of Motion The mass moment of iner…

, Chapter: 18 -Problem: 60 >> The uniform bar AB has a mass of 12 kg and is pin connected at A. If the support at B is remove (? = 90°), determine the velocity of the 5-kg block C at the instant the bar rotates downward to ? = 150°. Neglect the size and mass of the pulley at D. Transcribed Image Text: A -1 m Bo C D 1 m 1.5 m
Answer Preview: Geometry Hence block C rises BD 1 0 9319 …

, Chapter: 18 -Problem: 24 >> The 50-1b cylinder A is descending with a speed of 20 ft/s when the brake is applied. If wheel B must be brought to a stop after it has rotated 5 revolutions, determine the constant force P that must be applied to the brake arm. The coefficient of kinetic friction between the brake pad C and the wheel is ?k = 0.5. The wheel's weight is 25 lb, and the radius of gyration about its center of mass is
Answer Preview: Equilibrium Referring to Fig a we have Kinetic Energy and Work Sin…

, Chapter: 12 -Problem: 12 >> The sports car starts from rest and travels along a straight road. Its initial increasing acceleration is caused by the rear wheels of the car as shown on the graph. Construct the v-s graph. What is the velocity of the car when s=10 m and s=15m? Transcribed Image Text: a (m/s²) 10 5 10 15 s (m)
Answer Preview: The velocity time graph for the sports car can be constructed from the acceleration time …

, Chapter: 21 -Problem: 23 >> Show that if the angular momentum of a body is determined with respect to an arbitrary point A, then HA can be expressed by Eq. 21-9. This requires substituting ?A = ?G + ?G/A into Eq. 21-6 and expanding, noting that ??G dm = 0 by definition of the mass center and vG = vA + ? X ?G/A. Transcribed Image Text:
Answer Preview: Since pAdm X V L PA VA H U PG PG A dm …

, Chapter: 15 -Problem: 140 >> The jet is traveling at a speed of 720 km/h. If the fuel is being spent at 0.8 kg/s, and the engine takes in air at 200 kg/s, whereas the exhaust gas (air and fuel) has a relative speed of 12,000 m/s, determine the acceleration of the plane at this instant. The drag resistance of the air is FD = (55 v2), where the speed is measured in m/s. The jet has a mass of 7 Mg.
Answer Preview: Since the mass enters and exits the plane …

, Chapter: 12 -Problem: 156 >> A particle moves along a path defined by polar coordinates r = (2et) ft and ? = (8t2) rad, where t is in seconds. Determine the components of its velocity and acceleration when t = 1 s.
Answer Preview: When t 1 s r 2e 5 4366 j 2et 5 4366 …

, Chapter: 9 -Problem: 14 >> Locate the centroid y? of the area. Transcribed Image Text: y 4 m 1 x = 4 = 1/6 x ² -8 m-
Answer Preview: dA 4 y dx 1 6x dx …

, Chapter: 15 -Problem: 15 >> The 10-lb slider block is moving to the right with a velocity of 10 ft/s when it is acted upon by the forces F1 and F2. If the loading vary in the manner shown in the graph, determine the velocity of the block after 6 s. Neglect friction and the weight of the pulleys. Transcribed Image Text: F?? GL
Answer Preview: The impulse created by F 1 and F 2 ca…

, Chapter: 17 -Problem: 15 >> Determine the moment of inertia of the center crank about the x axis. The material is steel having a specific weight of ?st = 490 lb/ft3. Transcribed Image Text: 0.5 in.- ? 1 0.5 in. 0.5 in. 1 in. -0.5 in. 1 in. 0.5 in. ·X in. 1 in. 4 in. 1 in.
Answer Preview: ms mp Ix 490 32 2 490 32 2 2 TT 0 …

, Chapter: 18 -Problem: 6 >> The compound disk pulley consists of a hub and attached outer rim. If it has a mass of 3 kg and a radius of gyration of kG = 45 mm, determine the speed of block A after A descends 0.2 m from rest. Blocks A and B each have a mass of 2 kg. Neglect the mass of the cords. Transcribed Image Text: 30 mm-
Answer Preview: The speed of block A after it descends 0 2 m from rest can be determined using the conservation of e…

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, Chapter: 22 -Problem: 56 >> The engine is mounted on a foundation block which is spring supported. Describe the steady-state vibration if the block and engine have a total weight of 1500 lb, and the engine, when running, creates an impressed force F = (50 sin 2t) lb, where t is in seconds. Assume that the system vibrates only in the vertical direction, with the positive displacement measured downward, and that the total stif
Answer Preview: From the text the general sol…

, Chapter: 16 -Problem: 54 >> The crate is transported on a platform which rests on rollers, each having a radius r. If the rollers do not slip, determine their angular velocity if the platform moves forward with a velocity v. Transcribed Image Text: @
Answer Preview: Position Coordinate Equat…

, Chapter: 12 -Problem: 134 >> The motorcycle is traveling at a constant speed of 60 km h. Determine the magnitude of its acceleration when it is at point A. Transcribed Image Text: y -25 m- A y² = 2x -X
Answer Preview: Radius of Curvature Acceleration The speed of the moto…

, Chapter: 9 -Problem: 23 >> Locate the centroid x? of the area. Transcribed Image Text: y y = a h a²-x² +h h X
Answer Preview: Area and Moment Arm The area of t…

, Chapter: 15 -Problem: 21 >> If it takes 35 s for the 50-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest, determine the force of the rope on the tugboat. The propeller provides the propulsion force F on the tugboat which gives it forward motion, whereas the barge moves freely. Also, determine the magnitude of F. The barge has a mass of 75 Mg.
Answer Preview: System Barge A…

, Chapter: 17 -Problem: 4 >> The right circular cone is formed by revolving the shaded area around the x axis. Determine the moment of inertia Ix and express the result in terms of the total mass m of the cone. The cone has a constant density ?. Transcribed Image Text: y = 7x h -h- r X
Answer Preview: The mass of the disk e…

, Chapter: 21 -Problem: 65 >> Solve Prob. 21–64 when ? = 90°. Solve Prob. 21–64The top consists of a thin disk that has a weight of 8 lb and a radius of 0.3 ft. The rod has a negligible mass and a length of 0.5 ft. If the top is spinning with an angular velocity ?s = 300 rad/s, determine the steady-state precessional angular velocity ?p of the rod when ? = 40°.
Answer Preview: w 8 0 5 8 …

, Chapter: 12 -Problem: 25 >> If the effects of atmospheric resistance are accounted for, a freely falling body has an acceleration defined by the equation, a = 9.81[1- v²(10-4)] m/s², where v is in m/s and the positive direction is downward. If the body is released from rest at a very high altitude, determine (a) The velocity when t = 5 s, and (b) The body's terminal or maximum attainable velocity (as t ? ?).
Answer Preview: Velocity The velocity of the particle can be rel…

, Chapter: 21 -Problem: 31 >> The rod assembly has a mass of 2.5 kg/m and is rotating with a constant angular velocity of ? = {2k} rad/s when the looped end at C encounters a hook at S, which provides a permanent connection. Determine the angular velocity of the assembly immediately after impact. Transcribed Image Text: B x 0.5
Answer Preview: Angular momentum is co…

, Chapter: 16 -Problem: 3 >> The flywheel rotates with an angular velocity of ? = (4 ?¹/2) rad/s, where ? is in radians. Determine the time it takes to achieve an angular velocity of ? = 150 rad/s. When t = 0, ? = 1 rad. Transcribed Image Text: W
Answer Preview: The angular velocity of the flywheel can be expressed as 4 1 2 We want to find the time it …

, Chapter: 12 -Problem: 140 >> The car is traveling at a constant speed of 30 m/s. The driver then applies the brakes at A and thereby reduces the speed at the rate ofwhere t is in seconds. Determine the magnitude of the acceleration of the car just before it reaches point C on the circular curve. It takes 15 s for the car to travel from A to C. Transcr
Answer Preview: Velocity Using the initial condition v 30 m …

, Chapter: 9 -Problem: 58 >> The rectangular horn antenna is used for receiving microwaves. Determine the location x? of its center of  gravity G. The horn is made of plates having a constant thickness and density and is open at each end. Transcribed Image Text: 0.1 ft 0.3 ft -0.4 ft- -X- 30° +G 30° -0.6 ft- 0.3 ft
Answer Preview: ETA 2 0 2 0 3 0 4 2 0 2 0 1 0 4 2 0 7 0 …

, Chapter: 15 -Problem: 10 >> The force acting on a projectile having a mass m as it passes horizontally through the barrel of the cannon is F = C sin (?t/t?). Determine the projectile’s velocity when t = t?. If the projectile reaches the end of the barrel at this instant, determine the length s. Transcribed Image Text: S
Answer Preview: When t t m vx F …

, Chapter: 17 -Problem: 66 >> The kinetic diagram representing the general rotational motion of a rigid body about a fixed axis passing through O is shown in the figure. Show that IG? may be eliminated by moving the vectors m(aG)t and m(aG)t to point P, located a distance rGP = k2G/roG from the center of mass G of the body. Here kg represents the radius of gyration of the body about an axis passing through G. The point P is ca
Answer Preview: However …

, Chapter: 18 -Problem: 37 >> The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the distance the block must descend, starting from rest, in order to cause B to have an angular velocity of 6 rad/s. Neglect the mass of the cord and treat the pulleys as thin disks. No slipping occurs. Transc
Answer Preview: Vc WB 0 1 0 03 WA If B 6 ra…

, Chapter: 12 -Problem: 89 >> The girl at A can throw a ball at vA= 10 m/s. Calculate the maximum possible range R = Rmax and the associated angle ? at which it should be thrown. Assume the ball is caught at B at the same elevation from which it is thrown. Transcribed Image Text: VA = 10 m/s A -R B
Answer Preview: Thus Require s so …

, Chapter: 22 -Problem: 79 >> Draw the electrical circuit that is equivalent to the mechanical system shown. Determine the differential equation which describes the charge q in the circuit. Transcribed Image Text: m k C
Answer Preview: For the …

, Chapter: 16 -Problem: 52 >> When the bar is at the angle ?, the rod is rotating clockwise with constant angular velocity ?. Determine the velocity of the weight A at this instant. The cord is 20 ft long. Transcribed Image Text: 10 ft SA D A w, a 10 ft B
Answer Preview: Taking the time der…

, Chapter: 12 -Problem: 124 >> When the bicycle passes point A, it has a speed of 6 m/s, which is increasing at the rate of v? = (0.5) m/s². Determine the magnitude of its acceleration when it is at point A. Transcribed Image Text: y +50 m y = 12 In X 20
Answer Preview: Radius of Curvature Acceleration T…

, Chapter: 9 -Problem: 24 >> Locate the centroid y? of the area. Transcribed Image Text: y h y=-x²+h a- h X
Answer Preview: Area and Moment Arm The area of …

, Chapter: 15 -Problem: 2 >> A 20-lb block slides down a 30° inclined plane with an initial velocity of 2 ft/s. Determine the velocity of the block in 3 s if the coefficient of kinetic friction between the block and the plane is ?k = 0.25.
Answer Preview: x m vy Fydt m vy 1 0 N 3 20 …

, Chapter: 17 -Problem: 33 >> The motorcycle and rider have a total mass of 900 kg and mass center at G. Determine the minimum coefficient of static friction between the rear wheel and the slope in order for the rider to perform a “wheely,” that is, to begin to lift the front wheel off the road. Also, what is the corresponding acceleration? The front wheel is free to roll.
Answer Preview: Equations of Motion When wheely occurs the front wheel will …

, Chapter: 18 -Problem: 34 >> The spool has a mass of 100 kg and a radius of gyration of 400 mm about its center of mass O.If it is released from rest, determine its angular velocity after its center O has moved down the plane a distance of 2 m. The contact surface between the spool and the inclined plane is smooth.  Transcribed Image Text:
Answer Preview: Kinetic Energy and Work Referring to Fig a The mas…

, Chapter: 12 -Problem: 44 >> The v-t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure. The acceleration and deceleration that occur are constant and both have a magnitude of 4 m/s². If the plates are spaced 200 mm apart, determine the maximum velocity vmax and the time t' for the particle to travel from one plate to the other. Also draw the s-t graph. When t = t
Answer Preview: When s 0 1 m When t 0 447 s s 0 2 m ac …

, Chapter: 20 -Problem: 51 >> At the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity ?? = 6 rad/s, while at the same instant the arm is rotating upward at a constant rate ?? = 4 rad/s. If the conveyor is running at a rate r? = 5 ft/s, which is increasing at r? = 8 ft/s², determine the velocity and acceleration of the package P at the instant shown. Neglect the size o
Answer Preview: 6k rad s 0 To Vo ao 0 P O 41 rad s PIO 0 IP O 4 243j 4 243k ft VP O xyz P O xyz P O X IP …

, Chapter: 16 -Problem: 88 >> In an automobile transmission the planet pinions A and B rotate on shafts that are mounted on the planet-pinion carrier CD.As shown,CD is attached to a shaft at E which is aligned with the center of the fixed sun gear S. This shaft is not attached to the sun gear. If CD is rotating at ?CD = 8 rad/s, determine the angular velocity of the ring gear R.
Answer Preview: Pinion A WA VR …

, Chapter: 15 -Problem: 67 >> The 5-lb box B is dropped from rest 5 ft from the top of the 10-lb plate P, which is supported by the spring having a stiffness of k = 30 lb/ft. If e = 0.6 between the box and plate, determine the maximum compression imparted to the spring. Neglect the mass of the spring. Transcribed Image Text: B P
Answer Preview: Box Datum at P System Solvin…

, Chapter: 12 -Problem: 99 >> A projectile is fired from the platform at B. The shooter fires his gun from point A at an angle of 30°. Determine the muzzle speed of the bullet if it hits the projectile at C. Transcribed Image Text: B XXXXX - A 30° [1.8 m -20 m C 10 m
Answer Preview: Coordinate System The xy coordinate system will …

, Chapter: 9 -Problem: 91 >> Determine the outside surface area of the storage tank. Transcribed Image Text: 4 ft 30 ft -15 ft
Answer Preview: Surface Area Applying the theorem of P…

, Chapter: 17 -Problem: 81 >> Determine the angular acceleration of the 25-kg diving board, and the horizontal and vertical components of reaction at the pin A, the instant the man dives off. Assume that the board is uniform and rigid, and that at the instant he dives off, the spring is compressed a maximum amount of 200 mm, ? = 0, and the board is horizontal. Take k = 7 kN/m.
Answer Preview: Solving 6 I Aa 1 …

, Chapter: 17 -Problem: 7 >> The spool and wire wrapped around its core have a mass of 20 kg and a centroidal radius of gyration KG = 250 mm. If the coefficient of kinetic friction at the ground is ?B = 0.1, determine the angular acceleration of the spool when the 30-N-m couple moment is applied. Transcribed Image Text: 30 N-m
Answer Preview: The angular acceleration of the spool can be determined using the equation of rotational dynamics I …

, Chapter: 12 -Problem: 33 >> The car has a speed of 55 ft/s. Determine the angular velocity ? of the radial line OA at this instant. Transcribed Image Text: Ox r = 400 ft COMO A
Answer Preview: The angular velocity of a radial line OA at a given instant can be determ…

, Chapter: 22 -Problem: 71 >> The 10-kg block-spring-damper system is continually damped. If the block is displaced to x = 50 mm and released from rest, determine the time required for it to return to the position x = 2 mm. Transcribed Image Text: x k = 60 N/m 0000 € c = 80 N s/m G
Answer Preview: m 10 kg cc 2km x Aet Bet X1 2 2m 0 8377 c 80 2V 600 k …

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, Chapter: 15 -Problem: 70 >> Two identical balls A and B of mass m are suspended from cords of length L/2 and L, respectively. Ball A is released from rest when ? = 90° and swings down to ? = 0°, where it strikes B. Determine the speed of each ball just after impact and the maximum angle ? through which B will swing. The coefficient of restitution between the balls is e.
Answer Preview: Conservation of Energy First we will consider bob A …

, Chapter: 12 -Problem: 153 >> A car travels around a circular track having a radius of r = 300 m such that when it is at point A it has a velocity of 5 m/s, which is increasing at the rate of v? = (0.06t) m/s2, where t is in seconds. Determine the magnitudes of its velocity and acceleration when it has traveled one-third the way around the track. Trans
Answer Preview: Solve for the positive root a dv …

, Chapter: 10 -Problem: 16 >> Determine the moment of inertia for the area about the y axis. Transcribed Image Text: y 4 in. y² = = X 16 in. X
Answer Preview: Differential Element The moment of inertia …

, Chapter: 17 -Problem: 82 >> The turbine consists of a rotor which is powered from a torque applied at its center. At the instant the rotor is horizontal it has an angular velocity of 15 rad/s and a clockwise angular acceleration of 8 rad/s2. Determine the internal normal force, shear force, and moment at a section through A. Assume the rotor is a 50-m-long slender rod, having a mass of 3 kg/m.
Answer Preview: Fn m ac n NA 45 15 3 17 5 177kN F …

, Chapter: 17 -Problem: 74 >> The 5-kg cylinder is initially at rest when it is placed in contact with the wall B and the rotor at A. If the rotor always maintains a constant clockwise angular velocity ?= 6 rad/s, determine the initial angular acceleration of the cylinder. The coefficient of kinetic friction at the contacting surfaces B and C is ?k = 0.2.
Answer Preview: Equations of Motion The mass moment …

, Chapter: 12 -Problem: 11 >> A particle travels along a straight-line path such that in 4 s it moves from an initial position sA = -8 m to a position sB = +3 m. T hen in another 5 s it moves from sB to sC = -6 m. Determine the particle’s average velocity and average speed during the 9-s time interval.
Answer Preview: Average Velocity The displacement from A to C is s s C …

, Chapter: 21 -Problem: 38 >> Rod AB has a weight of 6 lb and is attached to two smooth collars at its end points by ball-and-socket joints. If collar A is moving downward at a speed of 8 ft/s, determine the kinetic energy of the rod at the instant shown. Transcribed Image Text: VA = 8 ft/s X 3 ft Z 2. 6 ft· 7 ft B 2 ft 1
Answer Preview: Equating i j and k components Als…

, Chapter: 16 -Problem: 28 >> The gear A on the drive shaft of the outboard motor has a radius rA = 0.7 in. and the meshed pinion gear B on the propeller shaft has a radius r? = 1.4 in. Determine the magnitudes of the velocity and acceleration of a point P located on the tip of the propeller at the instant t = 0.75 s. The drive shaft rotates with an angular acceleration ? = (300 ?t) rad/s², where t is in seconds. The propeller
Answer Preview: Angular Motion The angular velocity of gear A at t 0 75 s mu…

, Chapter: 15 -Problem: 125 >> Water is discharged from a nozzle with a velocity of 12 m/s and strikes the blade mounted on the 20-kg cart. Determine the tension developed in the cord, needed to hold the cart stationary, and the normal reaction of the wheels on the cart. The nozzle has a diameter of 50 mm and the density of water is ?w = 1000 kg/m3 Tran
Answer Preview: Steady Flow Equation Here the mass flow rate at sections A and …

, Chapter: 12 -Problem: 121 >> The car passes point A with a speed of 25 m/s after which its speed is defined by v = (25-0.15s) m/s, where s is in meters. Determine the magnitude of the car's acceleration when it reaches point B, where s = 51.5 m and x = 50 m. Transcribed Image Text: 16 m -y = 16 B 1 625 A X
Answer Preview: Velocity The speed of the car at B …

, Chapter: 5 -Problem: 88 >> Member AB is supported by a cable BC and at A by a square rod which fits loosely through the square hole at the end joint of the member as shown. Determine the components of reaction at A and the tension in the cable needed to hold the 800-lb cylinder in equilibrium. Transcribed Image Text: x 2 ft Z
Answer Preview: FBC FBC i Fx 0 F 0 F 0 0 0 0 …

, Chapter: 17 -Problem: 92 >> The uniform 150-lb beam is initially at rest when the forces ar

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