Determine the constant horizontal force f created by

Question

Question 1. The van is traveling at 20 km/h when the coupling of the trailer at A fails. If the trailer has a mass of 250 kg and coasts 45 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop.

Question 2. A block having a mass of 2 kg is placed on a spring scale located in an elevator that is moving downward. If the scale reading, which measures the force in the spring, is 20 N, determine the acceleration of the elevator. Neglect the mass of the scale.

Question 3. The baggage truck A has a mass of 800 kg and is used to pull the two cars, each with mass 300 kg. If the tractive force F on the truck is F = 480 N, determine the initial acceleration of the truck. What is the acceleration of the truck if the coupling at C suddenly fails? The car wheels are free to roll. Neglect the mass of the wheels.

Question 4. The man pushes on the 60-lb crate with a force F. The force is always directed down at 30° from the horizontal as shown, and its magnitude is increased until the crate begins to slide. Determine the crate's initial acceleration if the static coefficient of friction is μ_s = 0.6 and the kinetic coefficient of friction is μ_k = 0.3.

Question 5. A 40-lb suitcase slides from rest 20 ft down the smooth ramp. Determine the point where it strikes the ground at C. How long does it take to go from A to C?

Question 6. At a given instant the 10-lb block A is moving downward with a speed of 6 ft/s. Determine its speed 2 s later. Block B has a weight of 4 lb, and the coefficient of kinetic friction between it and the horizontal plane is μ_k = 0.2. Neglect the mass of the pulleys and cord.

Question 7. 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.

Question 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 μ_s = 0.2, determine the shortest time the belt can stop so that the package does not slide on the belt.

Question 9. The 2-lb collar C fits loosely on the smooth shaft. If the spring is unstretched when s = 0 and the collar is given a velocity of 15 ft/s, determine the velocity of the collar when s = 1 ft.

Question 10. The conveyor belt delivers each 12-kg crate to the ramp at A such that the crate's speed is v_A = 2.5 m/s, directed down along the ramp. If the coefficient of kinetic friction between each crate and the ramp is μ_k = 0.3, determine the speed at which each crate slides off the ramp at B. Assume that no tipping occurs. Take θ = 30°.

Question 11. 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.

Question 12. 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 up B. The coefficient of static friction between A and B is μ_s. Neglect any friction between B and C

Question 13. Determine the minimum speed at which the car can travel around the track without sliding down the slope.

Question 14. A girl, having a mass of 15 kg, sits motionless relative to the surface of a horizontal platform at a distance of r = 5 m from the platform's center. If the angular motion of the platform is slowly increased so that the girl's tangential component of acceleration can be neglected, determine the maximum speed which the girl will have before she begins to slip off the platform. The coefficient of static friction between the girl and the platform is μ = 0.2.

Question 15. Prove that if the block is released from rest at point B of a smooth path of arbitrary shape, the speed it attains when it reaches point A is equal to the speed it attains when it falls freely through a distance It; i.e., v = √(2gh).

Question 16. At the instant θ = 60°, the boy's center of mass G has a downward speed v_G = IS ft/s. Determine the rate of increase in his speed and the tension in each of the two supporting cords of the swing at this instant. The boy has a weight of 60 lb. Neglect his size and the mass of the seat and cords.

Question 17. At the instant θ = 60°, the boy's center of mass G is momentarily at rest. Determine his speed and the tension in each of the two supporting cords of the swing when θ = 90°. The boy has a weight of 60 lb. Neglect his size and the mass of the seat and cords.

Question 18. The block has a weight of 2 lb and it is free to move along the smooth slot in the rotating disk. The spring has a stiffness of 2.5 lb/ft and an unstretched length of 1.25 ft. Determine the force of the spring on the block and the tangential component of force which the slot exerts on the side of the block, when the block is at rest with respect to the disk and is traveling with a constant speed of 12 ft/s.

Question 19. If the bicycle and rider have a total weight of 180 lb, determine the resultant normal force acting on the bicycle when it is at point A while it is freely coasting at V_A = 6 ft/s. Also, compute the increase in the bicyclist's speed at this point. Neglect the resistance due to the wind and the size of the bicycle and rider.

Question 20. The 2-kg rod AB moves up and down as its end slides on the smooth contoured surface of the cam, where r = 0.1 m and z = (0.02 sin 2θ) m. If the cam is rotating at a constant rate of 5 rad/s, determine the maximum and minimum force the cam exerts on the rod.

Question 21. The boy of mass 40 kg is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r = 1.5 m, θ = (0.7t) rad, and z = (-0.5t) m, where t is in seconds. Determine the components of force F_r, F_θ, and F, which the slide exerts on him at the instant t = 2 s. Neglect the size of the boy.

Question 22. The collar, which has a weight of 3 lb, slides along the smooth rod lying in the horizontal plane and having the shape of a parabola r = 4/(1 - cosθ), where θ is in radians and r is in feet. if the collar's angular rate is constant and equals θ´ = 4 rad/s, determine the tangential retarding force P needed to cause the motion and the normal force that the collar exerts on the rod at the instant θ = 90°.

Question 23. The pilot of an airplane executes a vertical loop which in part follows the path of a cardioid, r = 600(1 + cos θ) ft, where θ is in radians. If his speed at A (θ = 0°) is a constant V_p = 80 ft/s, determine the vertical force the belt of his seat must exert on him to hold him to his seat when the plane is upside down at A. He weighs 150 lb.