Answer:
As the cart rolls down the hill from its elevated position, its mechanical energy is transformed from potential energy to kinetic energy. At a height just above the ground, the majority of the energy is in the form of kinetic energy. This is to say, energy due to vertical position has been transformed into energy due to motion. In fact, if air resistance can be neglected, then the amount of potential energy loss equals the amount of kinetic energy gained. Calculations can be performed to illustrate that the potential energy lost by the 3.0-kg cart in the above animation is equal to the kinetic energy gained. Assume that the height of the cart changes from 0.40 meters to 0.05 meters and the speed changes from 0 m/s to 2.62 m/s.
Explanation:
The PE Change = m*g*(height change)
PE Change = (3.0 kg)*(9.8 m/s/s)*(-0.40 m- 0.05 m)
PE Change = -10.3 J
KE Change = final 0.5*m*v^2 - init. 0.5*m*v^2
KE Change = 0.5*(3.0 kg)*(2.62 m/s)^2 - ) J
KE Change = 10.3 J
Thus, PE Change = -KE Change
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