Example 1: Following energy through a system
June 2015 (R) · Paper 1P · Question 11
Question 1
A student investigates how the energies of a ball and spring change when the ball and spring vibrate together.
The diagrams and bar charts show how the energies of the ball and spring vary with the position of the ball.
The ball has a mass of 1 kg.
GPE = gravitational potential energy of the ball (zero at ground level)
KE = kinetic energy of the ball
EPE = elastic potential energy of the spring
Use information from the diagrams and the bar charts to describe what happens to the energy, speed and position of the ball as it vibrates on the spring.
Final answer
As the ball moves from the top to the bottom of the spring, its GPE decreases and the spring’s EPE increases. At the top, the ball has 25 J of GPE, 1 J of EPE and zero KE. In the middle, its KE and speed are greatest: its KE is 4 J and its speed is 2.8 m/s. At the bottom, it has 5 J of GPE, 21 J of EPE and zero KE, so it is momentarily stationary at both ends of its motion. The total energy remains constant at 26 J. As the ball moves back up, the changes in the energy stores reverse.
Mark scheme points
Any six valid points are needed for full marks. This answer uses these six:
- M1 KE is zero at the top and bottom, and greatest (4 J) in the middle.
- M2 GPE is greatest (25 J) at the top and least (5 J) at the bottom.
- M3 EPE is least (1 J) at the top and greatest (21 J) at the bottom.
- M4 Total energy is constant in all three charts (26 J).
- M5 The ball’s speed is greatest in the middle.
- M6 The ball’s speed in the middle is 2.8 m/s.
Explanation
The ball is at its highest position at the top, so its GPE is greatest there. As it moves down, the spring stretches and stores more EPE. At the bottom, the ball is momentarily stationary, so its KE is zero; it is also momentarily stationary at the top.
The ball’s KE is greatest in the middle, so its speed is greatest there. Use the kinetic energy equation to find the speed:
KE = ½mv² 4 J = ½ × 1 kg × v² v = √(8 m²/s²) ≈ 2.8 m/s
The charts show that although the amounts in the energy stores change as the ball moves, their total remains 26 J.
Common mistakes
- Do not confuse the ball’s GPE with the spring’s EPE: GPE is greatest at the top, while EPE is greatest at the bottom.
- Do not say the ball is fastest at an endpoint; its KE and speed are greatest in the middle.
- Do not say the total energy changes: the charts show it stays constant while energy shifts between stores.