1. A pillbox hat is filled with toothpaste until it has a mass of 9.2 kg. An inquisitive engineering student is using a winch and rope to pull it up a ramp 3.2 m with a steady force of 97 N with the rope parallel to the ramp. If the ramp makes a 17° angle with the horizontal and the coefficient of kinetic friction between the ramp and the pillbox hat is 0.35 find how much energy/work: a) is done by gravity? b) is lost due to friction? c) is done by the steady force? d) What is the change in kinetic energy? e) after the 3.2 m what is the speed of the pillbox hat?
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- A 7.80-g bullet moving at 470 m/s penetrates a tree trunk to a depth of 5.60 cm.(a) Use work and energy considerations to find the average frictional force that stops the bullet.N (b) Assuming the friction force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.sA 7.80-g bullet moving at 560 m/s penetrates a tree trunk to a depth of 4.80 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.A 7.80-g bullet moving at 640 m/s penetrates a tree trunk to a depth of 6.10 cm. (a) Use work and energy considerations to find the average frictional force that stops the bullet. (b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.
- 4. This Olympic skeleton athlete slides down an icy track head first. The track has many twists and turns with a total height of 102.75 m. If the 99.375 kg man has a speed of 27 m/s at the bottom, what was the total work done on him by friction and air resistance slowing him down? (In other words, what was the energy lost to friction and air resistance?) He starts from rest at the top. Previous submissions:You may have noticed runaway truck lanes while driving in the mountains. These gravel-filled lanes are designed to stop trucks that have lost their brakes on mountain grades. Typically, such a lane is horizontal (if possible) and about 35.0 m long. Think of the ground as exerting a frictional drag force on the truck. A truck enters a typical runaway lane with a speed of 55.5 mph (24.8 m/s). Use the work-energy theorem to find the minimum coefficient of kinetic friction between the truck and the lane to be able to stop the truck.1. A 23.0 kg child is playing on a swing with a length of 2.5 m. If the swing starts from rest and makes an angle of 40.0◦ with the vertical at the top of the swing, a) determine the child’s speed at the bottom of the swing neglecting friction. b) If the swing has a speed of 2.8 m/s at the bottom, determine the work done by friction during the downswing and, bonus) assuming the force of friction is constant, determine the maximum angle the swing attains on the upswing after passing through the bottom. Hint: Use the approximation that cos θ ≈ 1 − 1 2 θ 2 for angles given in radians.