A 563 kg rollercoaster car starts at rest atop a 38-meter hill. Find the gravitational potential energy, when it goes over the second hill which is 14 meters high. You may assume the track is frictionless and that air resistance is negligible.

2

A 0.5 kg ball is thrown from the top of a 20 m high balcony at an angle of 45° and with a speed of 20 m/s. What is the mechanical energy of the ball when it is 10 m above the ground? Ignore air resistance. Take the 0 of potential energy to be when the ball is on the ground and use g = 10 m/s2.

A 76.0-kg hiker is descending a mountain that has a peak altitude of 2350 m above sea level. The hiker has a device that measures her potential energy, and when she is at the peak of the mountain she decides to "zero" it (that is, she set's the zero point of potential energy to be the mountaintop). What does her potential energy device read sometime later on her descent when she is 1960 m above sea level?

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?

The top of a descending ski slope is 50 m higher than the bottom of the slope. A 60-kg skier starts from rest and skis straight to the bottom of the slope. If 20% of the gravitational potential energy change of the skier  is converted into internal energy (due to friction and air drag), how fast is the 60-kg skier traveling at the bottom of the slope? Again, represent the process with work-energy bar charts indicating the system, the initial state, and the final state.

A 2.5 kg rock is released from rest at the surface of a pond 1.8m deep. As the rock falls, a constant upward force of 4.3N is exerted on it by water resistance. Let y=0 be at the bottom of the pond.A) Calculate the gravitational potential energy of the system, U, when the depth of the rock below the water's surface is 0.50 m.B) Calculate the kinetic energy of the rock, K, when the depth of the rock below the water's surface is 0.50m.C) Calculate the total mechanical energy of the system, E, when the depth of the rock below the water's surface is 0.50m.

A 0.40 kg block can slide up and down a rough 10-m-high, 30-m-long slope. At the bottom, a stiff spring with spring constant 800 N/m is compressed 0.50 m and used to launch the block up the slope. The friction force on the block from the slope is 1.2 N. What is the speed of the block when it reaches the top of the slope? When apply the following energy principle to this question, assuming the system is block+earth+spring+slope, which of the energy term is positive? Select all apply. ΔK + ΔUg + ΔUsp + ΔEth + ΔEch = Wexternal Answers choices      ΔK     ΔUg      ΔUsp     ΔEth      ΔEch     Wexternal

Justin, with a mass of 50 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 12 m/s. How much thermal energy is created by friction during his descent? Express your answer with the appropriate units. Eth = μA Value Units ?

"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?"