The Joker (another one of Batman\'s enemies) has a new toy: a spring-launched ca

Question

The Joker (another one of Batman's enemies) has a new toy: a spring-launched cart that delivers a high-explosive bomb underneath cars on street. The wheels use a unique air-bearing design in order to minimize friction. To test the wheels, Joker sets up the following experimental set up. The cart will begin at "A" with a certain velocity. Joker can then measure the velocities at "B" and "C." Use this information to answer the questions below. h_A = 10.0 m, the height at "A" h_B = 3.00 m, the height at "B" v_A = 2.00 m/s, the initial speed of the cart at "A" v_C = 10 m/s, the speed of the cart at "C"m = 7.00 kg, the mass of the cart What speed should the Joker expect to measure when the cart is at "B" v_B = What is the height at "C" h_C = In one of Joker's trial runs, a wheel axle broke, creating a significant amount of friction. In that particular trial, the speed of the cart at "B" was 8.93. How much energy was lost by the cart due to the friction. E_Lost =

Explanation / Answer

by conservation of energy

initial energy = final energy

mgh1 + 0.5 * mv1^2 = mgh2 + 0.5 * mv2^2

gh1 + 0.5 * v1^2 = gh2 + 0.5 * v2^2

9.8 * 10 + 0.5 * 2^2 = 9.8 * 3 + 0.5 * v2^2

v2 = 11.882 m/s

velocity at B = 11.882 m/s

9.8 * 10 + 0.5 * 2^2 = 9.8 * h + 0.5 * 10^2

h = 5.102 m

height at C = 5.102 m

9.8 * 10 + 0.5 * 2^2 = 9.8 * 3 + 0.5 * 8.93^2 + loss due to friction

loss due to friction = 30.727 J

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