Physics Demonstrations

Roller Coaster

Initial Height (m)
Hill 1 Height (m)
Hill 2 Height (m)

In this demonstration, a cart travels along a roller coaster track with an initial height ( $h_{0}$ ) and two subsequent hills of heights ( $h_{1}$ , $h_{2}$ ). The motion is governed by the conservation of mechanical energy. At any point on the track: $\frac{1}{2} m v^{2} + m g h = m g h_{0}$ Solving for the speed of the cart at any height $h$ : $v = \sqrt{2 g (h_{0} - h)}$ Note that the mass $m$ cancels — the speed depends only on the height difference, not the mass of the cart. The cart can only reach a hill if that hill's height is less than the initial height $h_{0}$ . If a hill exceeds $h_{0}$ , the cart will stop before reaching the peak. Some questions to consider while viewing the demonstration: What happens to the cart's speed at the bottom of a valley compared to the top of a hill? Set a hill height equal to the initial height. Does the cart make it over? What does this reveal about energy conservation? Since mass cancels out, would a heavier cart travel the same path at the same speed? Explain why or why not in a real-world scenario. Identify where on the track the cart has maximum kinetic energy and maximum potential energy.