A roller-coaster car of mass 1.50 x 10° kg is initially at the top of a rise at point @. It then moves 35.0 m at an angle of 50.0° below the horizontal to a lower point ®. (a) Find both the potential energy of the system when the car is at points @ and ® and the change in potential energy as the car moves from point @ to point ®, assuming y = 0 at point ®. (b) Repeat part (a), this time choosing y = 0 at point ©, which is another 15.0 m down the same slope from point ®.

Time yourself while running up a flight of steps, and compute the average rate at which you do work against the force of gravity. Express your answer in watts and in horsepower.

The figure below shows a plot of potential energy U versus position x of a 0.76 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are UA = 20.0 J, UB = 35.0 J, and Uc = 45.0 J. Uc UB UA 4 х (m) The particle is released at x = 4.5 m with an initial speed of 6.0 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? m (b) What are the magnitude and direction of the force on the particle as it begins to move to the left of x = 4.0 m? magnitude direction +X Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 6.0 m/s. (c) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? m (d) What are the magnitude and direction of the force on the particle as it begins to move to the right of x = 5.0 m? magnitude…

A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop).  c)What is the child's final speed, vf in m/s?

A 7.80-g bullet moving at 570 m/s penetrates a tree trunk to a depth of 4.40 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 60 kg box has an initial velocity of 12 m/s up a 60-degree inclined plane at an initial height of 0 meters. The coefficient of friction between the box and the ground is 0.2. [a] Calculate the box’s maximum height up the inclined plane. [b] Calculate the work done by friction. [c] If you increased the angle of the inclined plane, explain how that would affect the work done by friction.

A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop).  What is the child's final speed, vf in m/s?

A 0.42 kg particle has a speed of 5.0 m/s at point A and kinetic energy of 7.5 J at point B. (a) What is its kinetic energy at A? (b) What is its speed at point B? lea ng m/s (c) What is the total work done on the particle as it moves from A to B? Need Help? Read It ds.

A center throws a basketball m = 1 kg straight up with an initial speed of vo = 9.5 m's. He releases the ball at shoulder | height ho = 1.9 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height h it reaches, the mass m, and the gravitational acceleration g. E= What is the height, hm in meters? 9 HOME

"20 kg bear slides, from rest, 8 m down a Lodgepole Pine tree, moving with a speed of 5.6 m/s just before hitting the ground. What change occurs in the gravitational potential energy of the bear Earth system during the slide?"