5. A bead slides on a curved wire, starting from rest at point A in the figure below. If the wire is frictionless, find each of the following.

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1 Name: Work and Energy Problems Date: 1. A 2150 kg car moves down a level highway under the actions of two forces: a 1010 N forward force exerted on the drive wheels by the road and a 960 N resistive force. Determine the speed of the car after it has moved a distance of 35 m, assuming that it starts from rest. (1.28 m/s) 2. On a frozen pond, a sled is given a kick that imparts to it an initial speed of 2.0 m/s. The coefficient of kinetic friction between sled and ice is µ k = Use the work-energy theorem to find the distance the sled moves before coming to rest. (2.04 m) 3. A crate of mass 11.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 20.0 with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.10 m. What is the speed of the crate after being pulled 5.10 m? (4.82 m/s) (Don t use dynamics, use work and energy to solve) 4. A daredevil on a motorcycle leaves the end of a ramp with a speed of 38.0 m/s as in the figure below. If his speed is 36.4 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance. (6.07 m) 5. A bead slides on a curved wire, starting from rest at point A in the figure below. If the wire is frictionless, find each of the following. (a) the speed of the bead at B (9.9m/s) (b) the speed at C (7.67 m/s)

2 6. Tarzan swings on a 33.0 m long vine initially inclined at an angle of 30.0 with the vertical. (a) What is his speed at the bottom of the swing if he starts from rest? (9.31m/s) (b) What is the tension in the vine at the bottom of the swing if his mass is 85 kg? (1057N) (c) What is the tension in the rope at the bottom of the swing if he pushes off with a speed of 6.00 m/s? (1151N) 7. The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in the figure. If its spring is compressed a distance of m and the gun fired vertically as shown, the gun can launch a 15.0 g projectile to a maximum height of 24.0 m above the starting point of the ball (when its compressed). (a) Neglecting all resistive forces, determine the spring constant. (218 N/m) (b) Neglecting all resistive forces, determine the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in the diagram. (21.6 m/s) 8. A projectile is launched with a speed of 44 m/s at an angle of 57 above the horizontal. Use conservation of energy to find the maximum height reached by the projectile during its flight. (69.5 m) 9. A kg block is placed on a light vertical spring (k = N/m) and pushed downward, compressing the spring m. After the block is released, it leaves the spring and continues to travel upward. What height above the point of release will the block reach if air resistance is negligible? (7.48m) 10. A 82 kg diver steps off a 11 m tower and drops from rest straight down into the water. If he comes to rest 5.0 m beneath the surface, determine the average resistance force exerted on him by the water. (2570 N up )

3 11. A 21.0 kg child on a 1.00 m long swing is released from rest when the ropes of the swing make an angle of 25.0 with the vertical. (a) Neglecting friction, find the child's speed at the lowest position. (1.36 m/s) (b) What is the normal force acting on the child at the lowest point in the swing? (244.9N) (c) If the speed of the child at the lowest position is 1.20 m/s, what is the mechanical energy lost due to friction? (4.16 J) 12. A skier starts from rest at the top of a hill that is inclined at 9.8 with the horizontal. The hillside is 165 m long, and the coefficient of friction between snow and skis is At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest? (212 m) 13. A ski jumper starts from rest 48.0 m above the ground on a frictionless track and flies off the track at an angle of 45.0 above the horizontal and at a height of 18.0 m above the ground. Neglect air resistance. (a) What is her speed when she leaves the track? (24.2 m/s) (b) What is the maximum altitude she attains after leaving the track? (33 m) (c) Where does she land relative to the end of the track? (74.5 m) 14. A 931 kg vehicle is speeding along a twisting road. Coming around a corner the driver spots an accident across the road ahead. He, hits the brakes, but still collides at km/h. Without speeding (speed limit = 60 km/h) and under the same braking conditions he would have stopped just before hitting. How much faster than the speed limit was the car traveling? (25.7 km/h) 15. Suppose a 1-kg block is dropped from a height of 0.5 meter above an uncompressed spring. The spring has an elastic constant of 250 N/m and negligible mass. The block strikes the end of the spring and sticks to it. a. Determine the speed of the block at the instant it hits the end of the spring. (3.13 m/s) b. How far will the spring be compressed? (0.24 m)

4 16. a. Find the change in height between points B and C. (62m) b. How high is location D? (55.1m) c. How fast is the coaster moving at location E? (28.9 m/s) d. How far is the spring compressed from its hanging position? (5.9m) (Challenge question!) e. If the coaster traveled up the first hill in 1.2 min., how much power was used to pull it up the hill? ( W) Remember there is an initial speed at the bottom of the first hill. f. As shown in the figure at point D, the speed is 12 m/s and the force exerted by the track on the coaster is twice the weight of the coaster. What is the radius of the loop at D? (4.9m) g. At point C, the velocity of the coaster is 35 m/s, and the force exerted on the track by the coaster is four times the weight. What is the radius of the track at C? (41.6 m) Extra Practice: 17. A 74.0 kg base runner begins his slide into second base when he is moving at a speed of 3.6 m/s. The coefficient of friction between his clothes and Earth is He slides so that his speed is zero just as he reaches the base. (a) How much mechanical energy is lost due to friction acting on the runner? (480 J) (b) How far does he slide? (0.945m) 18. A 2.0 g bullet leaves the barrel of a gun at a speed of 335 m/s. Find the average force exerted by the expanding gases on the bullet as it moves the length of the 41 cm long barrel. The bullet starts from rest. (274 N)

5 19. A child and sled with a combined mass of 55.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 2.10 m/s at the bottom, what is the height of the hill? (0.225 m) 20. A 5.55 kg steel ball is dropped onto a copper plate from a height of 10.0 m. If the ball leaves a dent 2.60 mm deep in the plate, what is the average force exerted by the plate on the ball during the impact? ( N) 21. An airplane of mass kg is moving at 54 m/s. The pilot then revs up the engine so that the forward thrust by the air around the propeller becomes N. If the force exerted by air resistance on the body of the airplane has a magnitude of N, find the speed of the airplane after it has traveled 500 m. Assume that the airplane is in level flight throughout this motion. (79.7 m/s) 22. A kg car starts from rest at the top of a 5.8 m long driveway that is inclined at 17 with the horizontal. If an average friction force of N impedes the motion, find the speed of the car at the bottom of the driveway. (3.34 m/s) 23. A diver jumps from a height of 2.59 m with an initial speed of 0.8 m/s. What is his speed entering the water? (7.17 m/s) 24. How far must a 82.9 kg box be pushed across the floor to reach a speed of m/s if the pushing force is N, the coefficient of kinetic friction between the box and the floor is 0.27 and it is starting from rest? (2.03 m) (not 9.09 m) 25. If a 19.7 kg box is pushed across the floor with a force of 87.3 N, what is its speed after 5.57 m if the coefficient of kinetic friction between the box and the floor is 0.38 and it is starting from rest? (2.8 m/s) (not m/s) 26. A 63.5 kg box is pushed across the floor with a force of N. What is the coefficient of kinetic friction between the box and the floor if it is starting from rest and reaches a speed of m/s after being pushed 2.57 m? (0.49) 27. Find the unknown quantities at various points of the frictionless rollercoaster ride shown below. (28.6 m, 5.34m/s, 23.61m/s, 27.2m, 17.4m/s) V= 3m/s V =? v = 8 m/s V = 6m/s h=30m h =? v =? h= 29 m V=? h =? h = 15m h=2 m