Question

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a student measures how high a roller coaster cart rises on each hill after the first drop. question: why does the cart not rise as high on each following hill? use energy transfer and conversion in your explanation.

Explanation:

When the roller - coaster cart moves, energy is transferred and converted. At the top of the first hill, it has gravitational potential energy ($E_p = mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height). As it moves down and up subsequent hills:

• There is friction between the cart and the track. Friction causes some of the mechanical energy (the sum of potential and kinetic energy) to be converted into thermal energy (heat) and sound energy.
• According to the law of conservation of energy, the total energy of the system (cart + track + surrounding air) is conserved. But the available mechanical energy for the cart to reach the same height as the previous hill decreases because of the energy losses (due to non - conservative forces like friction). So, the gravitational potential energy at the top of each subsequent hill ($E_p=mgh$, with $m$ and $g$ constant) is less, which means $h$ (height) is less.

Answer:

The cart does not rise as high on each following hill because of energy losses. Some of the mechanical energy (gravitational potential energy at the start) is converted into non - mechanical forms (thermal and sound energy) due to friction (a non - conservative force). As a result, the available mechanical energy (which determines the height through the formula $E_p = mgh$, with $m$ and $g$ constant) for the cart to reach the same height as the previous hill is reduced.