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engineering
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Engineering Mechanics Dynamics 14th Global Edition Hibbeler - Solutions

F13–8. Determine the maximum speed that the jeep can travel over the crest of the hill and not lose contact with the road. p = 75m + Prob. F13-8
F13–7. The block rests at a distance of 2 m from the center of the platform. If the coefficient of static friction between the block and the platform is ms = 0.3, determine the maximum speed which the block can attain before it begins to slip.Assume the angular motion of the disk is slowly
P13–6. Set up the n,b, t axes and write the equations of motion for the 10-kg block along each of these axes. 4 m 14 = 0.2 8 m/s (a)
P13–5. Set up the n, t axes and write the equations of motion for the 10-kg block along each of these axes. M = 0.2 10 m 6 m/s (a) 30% 4 m/s 5 m P = 0.3
13–51. The block A has a mass mA and rests on the pan B, which has a mass mB. Both are supported by a spring having a stiffness k that is attached to the bottom of the pan and to the ground. Determine the distance d the pan should be pushed down from the equilibrium position and then released
13–50. Block A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having a mass mB, is pressed against A so that the spring deforms a distanced, show that for separation to occur it is necessary that d 7 2mkg(mA + mB ) >k, where mk is
13–49. Block A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having a mass mB, is pressed against A so that the spring deforms a distanced, determine the distance both blocks slide on the smooth surface before they begin to separate.
*13–48. The smooth block B of negligible size has a mass m and rests on the horizontal plane. If the board AC pushes on the block at an angle u with a constant acceleration a0, determine the velocity of the block along the board and the distance s the block moves along the board as a function of
13–47. Blocks A and B each have a mass m. Determine the largest horizontal force P which can be applied to B so that A will not slip on B. The coefficient of static friction between A and B is ms. Neglect any friction between B and C. A 8 B C Probs. 13-46/47 P
The 10-kg block shown in Fig. 14–6a rests on the smooth incline. If the spring is originally stretched 0.5 m, determine the total work done by all the forces acting on the block when a horizontal force P = 400 N pushes the block up the plane s = 2 m. 2 sin 30 m s=2m P=400 N Initial position of
13–46. Blocks A and B each have a mass m. Determine the largest horizontal force P which can be applied to B so that A will not move relative to B. All surfaces are smooth. A 8 B C Probs. 13-46/47 P
13–45. Each of the three plates has a mass of 10 kg. If the coefficients of static and kinetic friction at each surface of contact are ms = 0.3 and mk = 0.2, respectively, determine the acceleration of each plate when the three horizontal forces are applied. 18 N D C 100 N 15 N B A Prob. 13-45
*13–44. A parachutist having a mass m opens his parachute from an at-rest position at a very high altitude. If the atmospheric drag resistance is FD = kv 2, where k is a constant, determine his velocity when he has fallen for a time t. What is his velocity when he lands on the ground?This
13–43. If the force exerted on cable AB by the motor is F = (100t 3>2) N, where t is in seconds, determine the 50-kg crate’s velocity when t = 5 s. The coefficients of static and kinetic friction between the crate and the ground are ms = 0.4 and mk = 0.3, respectively. Initially the crate is
13–42. If the motor draws in the cable with an acceleration of 3 m>s2, determine the reactions at the supports A and B.The beam has a uniform mass of 30 kg>m, and the crate has a mass of 200 kg. Neglect the mass of the motor and pulleys. A 2.5 m 0.5 m 3 m/s C 3 m Prob. 13-42 B
13–41. A freight elevator, including its load, has a mass of 1 Mg. It is prevented from rotating due to the track and wheels mounted along its sides. If the motor M develops a constant tension T = 4 kN in its attached cable, determine the velocity of the elevator when it has moved upward 6 m
*13–40. The tractor is used to lift the 150-kg load B withthe 24-m-long rope, boom, and pulley system. If the tractor travels to the right with an acceleration of 3 m>s2 and has a velocity of 4 m>s at the instant sA = 5 m, determine the tension in the rope at this instant. When sA = 0, sB =
13–39. The tractor is used to lift the 150-kg load B with the 24-m-long rope, boom, and pulley system. If the tractor travels to the right at a constant speed of 4 m>s, determine the tension in the rope when sA = 5 m. When sA = 0, sB = 0. SB B 12 m Probs. 13-39/40
13–38. Blocks A and B each has a mass m. Determine the largest horizontal force P which can be applied to B so that it will not slide on A. Also, what is the corresponding acceleration? The coefficient of static friction between A and B is ms. Neglect any friction between A and the horizontal
13–37. The 10-kg block A rests on the 50-kg plate B in the position shown. Neglecting the mass of the rope and pulley, and using the coefficients of kinetic friction indicated, determine the time needed for block A to slide 0.5 m on the plate when the system is released from rest. 0.5 m HAB=0.2 4
*13–36. A car of mass m is traveling at a slow velocity v0.If it is subjected to the drag resistance of the wind, which is proportional to its velocity, i.e., FD = kv, determine the distance and the time the car will travel before its velocity becomes 0.5v0. Assume no other frictional forces act
13–35. An electron of mass m is discharged with an initial horizontal velocity of v0. If it is subjected to two fields of force for which Fx = F0 and Fy = 0.3F0, where F0 is constant, determine the equation of the path, and the speed of the electron at any time t. +++++++ ++++ Vo Prob. 13-35 +++
13–34. The 300-kg bar B, originally at rest, is being towed over a series of small rollers. Determine the force in the cable when t = 5 s, if the motor M is drawing in the cable for a short time at a rate of v = (0.4t2) m>s, where t is in seconds (0 … t … 6 s). How far does the bar move in
13–33. The coefficient of static friction between the 200-kg crate and the flat bed of the truck is ms = 0.3. Determine the shortest time for the truck to reach a speed of 60 km>h, starting from rest with constant acceleration, so that the crate does not slip. Prob. 13-33
*13–32. The 4-kg smooth cylinder is supported by the spring having a stiffness of kAB = 120 N>m. Determine the velocity of the cylinder when it moves downward s = 0.2 m from its equilibrium position, which is caused by the application of the force F = 60 N. F = 60 N T S B KAB = 120 N/m A Prob.
13–31. Crate B has a mass m and is released from rest when it is on top of cart A, which has a mass 3m. Determine the tension in cord CD needed to hold the cart from moving while B is sliding down A. Neglect friction. D B Prob. 13-31 A
13–30. The 1.5 Mg sports car has a tractive force of F = 4.5 kN. If it produces the velocity described by v-t graph shown, plot the air resistance R versus t for this time period. 45 R F v (m/s) v = (-0.051+3t) m/s Prob. 13-30 30 t(s)
13–29. The conveyor belt is moving downward at 4 m>s.If the coefficient of static friction between the conveyor and the 15-kg package B is ms = 0.8, determine the shortest time the belt can stop so that the package does not slide on the belt. B 4m/s 30 Prob. 13-29
*13–28. The conveyor belt delivers each 12-kg crate to the ramp at A such that the crate’s speed is vA = 2.5 m>s, directed down along the ramp. If the coefficient of kinetic friction between each crate and the ramp is mk = 0.3, determine the smallest incline u of the ramp so that the crates
13–27. The conveyor belt delivers each 12-kg crate to the ramp at A such that the crate’s speed is vA = 2.5 m>s, directed down along the ramp. If the coefficient of kinetic friction between each crate and the ramp is mk = 0.3, determine the speed at which each crate slides off the ramp at B.
13–25. A 60-kg suitcase slides from rest 5 m down the smooth ramp. Determine the distance R where it strikes the ground at B. How long does it take to go from A to B?13–26. Solve Prob. 13–25 if the suitcase has an initial velocity down the ramp of vA = 2 m>s, and the coefficient of kinetic
*13–24. If the supplied force F = 150 N, determine the velocity of the 50-kg block A when it has risen 3 m, starting from rest. B F A Prob. 13-24
13–23. The 50-kg block A is released from rest. Determine the velocity of the 15-kg block B in 2 s. B E A Prob. 13-23
13–22. The bullet of mass m is given a velocity due to gas pressure caused by the burning of powder within the chamber of the gun. Assuming this pressure creates a force of F = F0 sin (pt>t0) on the bullet, determine the velocity of the bullet at any instant it is in the barrel. What is the
13–21. The force of the motor M on the cable is shown in the graph. Determine the velocity of the 400-kg crate A when t = 2 s. M F(N) 2500- -F=62512 -1 (s) 2 A Prob. 13-21
*13–20. Determine the required mass of block A so that when it is released from rest it moves the 5-kg block B 0.75 m up along the smooth inclined plane in t = 2 s.Neglect the mass of the pulleys and cords. A E C 60 Prob. 13-20 B
13–19. A crate having a mass of 60 kg falls horizontally off the back of a truck which is traveling at 80 km>h.Determine the coefficient of kinetic friction between the road and the crate if the crate slides 45 m on the ground with no tumbling along the road before coming to rest. Assume that
13–18. The motor lifts the 50-kg crate with an acceleration of 6 m>s2. Determine the components of force reaction and the couple moment at the fixed support A. A y 4 m B 30 16 m/s Prob. 13-18 x
13–17. Determine the acceleration of the blocks when the system is released. The coefficient of kinetic friction is mk, and the mass of each block is m. Neglect the mass of the pulleys and cord. A B Prob. 13-17
*13–16. The 2-Mg truck is traveling at 15 m>s when the brakes on all its wheels are applied, causing it to skid for a distance of 10 m before coming to rest. Determine the constant horizontal force developed in the coupling C, and the frictional force developed between the tires of the truck
13–15. The 75-kg man pushes on the 150-kg crate with a horizontal force F. If the coefficients of static and kinetic friction between the crate and the surface are ms = 0.3 and mk = 0.2, and the coefficient of static friction between the man’s shoes and the surface is ms = 0.8, show that the
13–14. The 400-kg mine car is hoisted up the incline using the cable and motor M. For a short time, the force in the cable is F = (3200t2) N where t is in seconds. If the car has an initial velocity v1 = 2 m>s at s = 0 and t = 0, determine the distance it moves up the plane when t = 2 s. v = 2
13–13. The 400-kg mine car is hoisted up the incline using the cable and motor M. For a short time, the force in the cable is F = (3200t2) N, where t is in seconds. If the car has an initial velocity v1 = 2 m>s when t = 0, determine its velocity when t = 2 s. v = 2 m/s M 17 15 Probs. 13-13/14
*13–12. The elevator E has a mass of 500 kg and the counterweight at A has a mass of 150 kg. If the elevator attains a speed of 10 m>s after it rises 40 m, determine the constant force developed in the cable at B. Neglect the mass of the pulleys and cable. A E B Prob. 13-12
13–11. Cylinder B has a mass m and is hoisted using the cord and pulley system shown. Determine the magnitude of force F as a function of the block’s vertical position y so that when F is applied, the block rises with a constant acceleration aB. Neglect the mass of the cord and pulleys. F d.
13–10. The winding drum D is drawing in the cable at an accelerated rate of 5 m>s2. Determine the cable tension if the suspended crate has a mass of 800 kg. Prob. 13-10
13–9. The conveyor belt is designed to transport packages of various weights. Each 10-kg package has a coefficient of kinetic friction mk = 0.15. If the speed of the conveyor is 5 m>s, and then it suddenly stops, determine the distance the package will slide on the belt before coming to rest.
*13–8. The conveyor belt is moving at 4 m>s. If the coefficient of static friction between the conveyor and the 10-kg package B is ms = 0.2, determine the shortest time the belt can stop so that the package does not slide on the belt. B Probs. 13-8/9
13–7. If the 50-kg crate starts from rest and achieves a velocity of v = 4 m>s when it travels a distance of 5 m to the right, determine the magnitude of force P acting on the crate. The coefficient of kinetic friction between the crate and the ground is mk = 0.3. Probs. 13-6/7 30
13–6. If the coefficient of kinetic friction between the 50-kg crate and the ground is mk = 0.3, determine the distance the crate travels and its velocity when t = 3 s.The crate starts from rest, and P = 200 N. Probs. 13-6/7 30
13–5. If the 50-kg crate starts from rest and travels a distance of 6 m up the plane in 4 s, determine the magnitude of force P acting on the crate. The coefficient of kinetic friction between the crate and the ground is mk = 0.25. P 30 Probs. 13-4/5 30
*13–4. If P = 400 N and the coefficient of kinetic friction between the 50-kg crate and the inclined plane is mk = 0.25, determine the velocity of the crate after it travels 6 m up the plane.The crate starts from rest. P 30 Probs. 13-4/5 30
13–3. If blocks A and B of mass 10 kg and 6 kg respectively, are placed on the inclined plane and released, determine the force developed in the link. The coefficients of kinetic friction between the blocks and the inclined plane are mA = 0.1 and mB = 0.3. Neglect the mass of the link. A Prob.
13–2. The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20° from the horizontal as shown. Determine the crate’s acceleration in t = 2 s if the coefficient of static friction is ms = 0.4, the coefficient of kinetic friction is mk = 0.3, and the towing force
13–1. The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20° from the horizontal as shown. If the magnitude of P is increased until the crate begins to slide, determine the crate’s initial acceleration if the coefficient of static friction is ms = 0.5 and
F13–6. Block B rests upon a smooth surface. If the coefficients of static and kinetic friction between A and B are ms = 0.4 and mk = 0.3, respectively, determine the acceleration of each block if P = 30 N. 10 kg P A B Prob. F13-6 25 kg
F13–5. The spring has a stiffness k = 200 N>m and is unstretched when the 25-kg block is at A. Determine the acceleration of the block when s = 0.4 m. The contact surface between the block and the plane is smooth. 0.3 m A F= 100 N F = 100 N k = 200 N/m Prob. F13-5
F13–4. The 2-Mg car is being towed by a winch. If the winch exerts a force of T = 100(s + 1) N on the cable, where s is the displacement of the car in meters, determine the speed of the car when s = 10 m, starting from rest.Neglect rolling resistance of the car. Prob. F13-4
F13–3. A spring of stiffness k = 500 N>m is mounted against the 10-kg block. If the block is subjected to the force of F = 500 N, determine its velocity at s = 0.5 m. When s = 0, the block is at rest and the spring is uncompressed.The contact surface is smooth. F = 500 N S k = 500 N/m wwwwwwww
F13–2. If motor M exerts a force of F = (10t2 + 100) N on the cable, where t is in seconds, determine the velocity of the 25-kg crate when t = 4 s. The coefficients of static and kinetic friction between the crate and the plane are ms = 0.3 and mk = 0.25, respectively. The crate is initially at
F13–1. The motor winds in the cable with a constant acceleration, such that the 20-kg crate moves a distance s = 6 m in 3 s, starting from rest. Determine the tension developed in the cable. The coefficient of kinetic friction between the crate and the plane is mk = 0.3. A 30 Prob. F13-1 M
R12–11. Two planes, A and B, are flying at the same altitude. If their velocities are vA = 600 km>h and vB = 500 km>h such that the angle between their straightline courses is u = 75, determine the velocity of plane B with respect to plane A. 8. VB Prob. R12-11 B
R12–10. Determine the time needed for the load at B to attain a speed of 8 m>s, starting from rest, if the cable is drawn into the motor with an acceleration of 0.2 m>s2. B B Prob. R12-10
R12–9. A particle is moving along a circular path of 2-m radius such that its position as a function of time is given by u = (5t2) rad, where t is in seconds. Determine the magnitude of the particle’s acceleration when u = 30°. The particle starts from rest when u = 0°.
R12–8. Car B turns such that its speed is increased by(at)B = (0.5et) m>s2, where t is in seconds. If the car starts from rest when u = 0, determine the magnitudes of its velocity and acceleration when t = 2 s. Neglect the size of the car. A B 5 m Prob. R12-8
R12–7. The truck travels in a circular path having a radius of 50 m at a speed of v = 4 m>s. For a short distance from s = 0, its speed is increased by v # = (0.05s) m>s2, where s is in meters. Determine its speed and the magnitude of its acceleration when it has moved s = 10 m. v = (0.05s)
R12–6. From a videotape, it was observed that a player kicked a football 40 m during a measured time of 3.6 seconds. Determine the initial speed of the ball and the angle u at which it was kicked. 40 m Prob. R12-6
R12–5. A car traveling along the straight portions of the road has the velocities indicated in the figure when it arrives at points A, B, and C. If it takes 3 s to go from A to B, and then 5 s to go from B to C, determine the average acceleration between points A and B and between points A and C.
R12–4. The v–t graph of a car while traveling along a road is shown. Determine the acceleration when t = 2.5 s, 10 s, and 25 s. Also if s = 0 when t = 0, find the position when t = 5 s, 20 s, and 30 s. v (m/s) 20- 20 - 20 Prob. R12-4 t(s) 30
R12–2. If a particle has an initial velocity v0 = 12 m>s to the right, and a constant acceleration of 2 m>s2 to the left, determine the particle’s displacement in 10 s. Originally s0 = 0.R12–3. A projectile, initially at the origin, moves along a straight-line path through a fluid medium such
R12–1. The position of a particle along a straight line is given by s = (t 3 - 9t 2 + 15t) m, where t is in seconds.Determine its maximum acceleration and maximum velocity during the time interval 0 … t … 10 s.
C12–4. The pilot tells you the wingspan of her plane and her constant airspeed. How would you determine the acceleration of the plane at the moment shown? Use numerical values and take any necessary measurements from the photo. Prob. C12-4
C12–3. The basketball was thrown at an angle measured from the horizontal to the man’s outstretched arm. If the basket is 3 m from the ground, make appropriate measurements in the photo and determine if the ball located as shown will pass through the basket. Prob. C12-3
C12–2. If the sprinkler at A is 1 m from the ground, then scale the necessary measurements from the photo to determine the approximate velocity of the water jet as it flows from the nozzle of the sprinkler. Prob. C12-2
C12–1. If you measured the time it takes for the construction elevator to go from A to B, then B to C, and then C to D, and you also know the distance between each of the points, how could you determine the average velocity and average acceleration of the elevator as it ascends from A to D? Use
F12–26. A projectile is fired with an initial velocity of vA = 150 m>s off the roof of the building. Determine the range R where it strikes the ground at B. y VA = 150 m/s -R. B Prob. F12-26 150 m x
F12–25. A ball is thrown from A. If it is required to clear the wall at B, determine the minimum magnitude of its initial velocty vA. 0.9 m 30 -x 2.4 m -3.6 m Prob. F12-25 -x
F12–24. Water is sprayed at an angle of 90 from the slope at 20 m>s. Determine the range R. Prob. F12-24 Un = 20 m/s
F12–23. 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. 30 1.5 m -x -10 m- Prob. F12-23 3 m
F12–22. The ball is kicked from point A with the initial velocity vA = 10 m>s. Determine the range R, and the speed when the ball strikes the ground. XB- V = 10 m/s B 30 Prob. F12-21/22 x
F12–21. The ball is kicked from point A with the initial velocity vA = 10 m>s. Determine the maximum height h it reaches.
F12–20. The box slides down the slope 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
F12–19. A particle is traveling along the parabolic path y = 0.25x2. If x = 8 m, vx = 8 m>s, and ax = 4 m>s2 when t = 2 s, determine the magnitude of the particle’s velocity and acceleration at this instant. Prob. F12-19 y = 0.25x -x
F12–18. A particle travels along a straight-line path y = 0.5x. If the x component of the particle’s velocity is vx = (2t2) m>s, where t is in seconds, determine the magnitude of the particle’s velocity and acceleration when t = 4 s. y=0.5x Prob. F12-18 -x
F12–17. A particle is constrained to travel along the path.If x = (4t4) m, where t is in seconds, determine the magnitude of the particle’s velocity and acceleration when t = 0.5 s. = 4x x (4) m Prob. F12-17 x
F12–16. A particle is traveling along the straight path. If its position along the x axis is x = (8t) m, where t is in seconds, determine its speed when t = 2 s. 3 m -x 81- y= 0.75x 4 m Prob. F12-16 x
F12–15. If the x and y components of a particle’s velocity are vx = (32t) m>s and vy = 8m>s, determine the equation of the path y = f(x), if x = 0 and y = 0 when t = 0.
P12–6. The particle travels from A to B. Identify the three unknowns, and write the three equations needed to solve for them. A 60 m/s 20 LAB=5S Prob. P12-6 B x
P12–5. The particle travels from A to B. Identify the three unknowns, and write the three equations needed to solve for them. 8 m A 10 m/s 30 Prob. P12-5 B x
P12–4. The particle travels from A to B. Identify the three unknowns, and write the three equations needed to solve for them. y A 40 m/s 20 m Prob. P12-4 B x
P12–3. Use the chain-rule and find y · and ¨y in terms of x, x · and ¨x ifa) y = 4x2b) y = 3exc) y = 6 sin x
12–235. The ship travels at a constant speed of vs = 20 m>s and the wind is blowing at a speed of vw = 10 m>s, as shown. Determine the magnitude and direction of the horizontal component of velocity of the smoke coming from the smoke stack as it appears to a passenger on the ship. 130 v =
12–234. Car B is traveling along the curved road with a speed of 15 m>s while decreasing its speed at 2 m>s2. At this same instant car C is traveling along the straight road with a speed of 30 m>s while decelerating at 3 m>s2. Determine the velocity and acceleration of car B relative
12–233. Car A travels along a straight road at a speed of 25 m>s while accelerating at 1.5 m>s2. At this same instant car C is traveling along the straight road with a speed of 30 m>s while decelerating at 3 m>s2. Determine the velocity and acceleration of car A relative to car C.
*12–232. At a given instant the football player at A throws a football C with a velocity of 20 m>s in the direction shown.Determine the constant speed at which the player at B must run so that he can catch the football at the same elevation at which it was thrown. Also calculate the relative
12–231. At the instant shown, car A travels along the straight portion of the road with a speed of 25 m>s. At this same instant car B travels along the circular portion of the road with a speed of 15 m>s. Determine the velocity of car B relative to car A. 15% p=200 m A 301 B 15 Prob. 12-231
12–230. A man walks at 5 km>h in the direction of a 20 km>h wind. If raindrops fall vertically at 7 km>h in still air, determine direction in which the drops appear to fall with respect to the man. v = 20 km/h vm = 5 km/h Prob. 12-230
12–229. At the instant shown, cars A and B are traveling at velocities of 40 m>s and 30 m>s, respectively. If A is increasing its speed at 4 m>s2, whereas the speed of B is decreasing at 3 m>s2, determine the velocity and acceleration of B with respect to A. The radius of curvature at
12–228. At the instant shown, cars A and B are traveling at velocities of 40 m>s and 30 m>s, respectively. If B is increasing its velocity by 2 m>s2, while A maintains a constant velocity, determine the velocity and acceleration of B with respect to A. The radius of curvature at B is rB = 200 m.
12–227. A passenger in an automobile observes that raindrops make an angle of 30° with the horizontal as the auto travels forward with a speed of 60 km>h. Compute the terminal (constant) velocity vr of the rain if it is assumed to fall vertically. Prob. 12-227 60 km/h

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