Warm-up: Conservation of energy during an elastic bounce
Conservation of Energy: Warm-up
Imagine dropping a ball from a height y = h above the ground. Define your coordinate system such that y = 0 m is ground-level. Use this information to fill in the chart below. Do so under the assumption that we can ignore air resistance, and as a result, we take mechanical energy to be conserved.
Think about it:
i) Take some time to reflect on whether you needed the mass of the ball to do the previous exercise.
ii) When the ball impacts the ground, it bounces back up. Let’s assume that the collision with the floor is perfectly elastic, that is, all the mechanical energy is conserved. What does this mean about the speed of the ball just before and just after the ball bounces? How high will the ball bounce? (Helpful hint: You don’t need to do any calculations to solve either of these questions.)
To be precise, let’s imagine what happens during the collision of the ball with the floor. Microscopically, the floor deforms ever so slightly because it is hard and the ball deforms much more because it is softer. If the energy is conserved during the bounce, then all the energy that goes into deforming the floor and the ball (elastic energy) gets returned to the kinetic energy, K, of the ball. In this lab, we will use the equations you derived above to help us understand what happens to the energy during successive bounces of a ball. While the scenario above described a perfect elastic collision with the floor, meaning mechanical energy was conserved, realistically some energy is lost to other forms. Some examples include friction and sound (after all, you hear the ball impact the ground, meaning energy was lost to sound).
Before moving on!
Make sure you have done all necessary calculations and understood the topics discussed in the examples! They will be useful in the exercises to come.
