Question

Investigators studying the effect of hitting a soccer ball with the head are using a force plate to look at the forces in ball collisions; the force when the ball hits a player’s head will be similar. A 0.43 kg ball is launched at a force plate at 16 m/s. Smoothed data for the force versus time for the collision are shown in Figure P9.12. At what speed does the ball rebound from the plate?

Answer 1

Answer: To determine the speed at which the ball rebounds from the plate, we need to analyze the force versus time graph shown in Figure P9.12. By examining the graph, we can identify the point at which the ball collides with the force plate and the subsequent rebound.

Here are the steps to find the rebound speed:

Explanation:

1. Locate the point of impact: On the force versus time graph, find the point where the force spikes or reaches its maximum value. This corresponds to the moment of collision between the ball and the force plate.

2. Determine the time of impact: From the x-axis of the graph, identify the time at which the maximum force occurs. Note down this value.

3. Analyze the rebound phase: After the collision, observe the force curve as it decreases and eventually returns to zero. This represents the rebound phase of the ball.

4. Find the time of rebound: Locate the point on the graph where the force returns to zero. Note down the time at which this occurs.

5. Calculate the rebound speed: To calculate the rebound speed, we need to know the duration of the collision. This can be determined by subtracting the time of impact (step 2) from the time of rebound (step 4). Let's call this duration 't'.

Next, we use the principle of conservation of momentum, which states that the total momentum before and after the collision is the same.

Momentum before collision = Momentum after collision

The momentum before the collision is given by the mass of the ball (0.43 kg) multiplied by its initial velocity (16 m/s).

Momentum after the collision is given by the mass of the ball multiplied by its rebound velocity, which we'll call 'v'.

Therefore, we have: (0.43 kg) * (16 m/s) = (0.43 kg) * (v)

Solve this equation to find the rebound velocity 'v'.

Once you have the rebound velocity, you have the speed at which the ball rebounds from the plate.

Remember to include appropriate units (such as m/s) in your final answer.

Note: Since we don't have access to Figure P9.12, it's not possible to provide an exact numerical answer. However, by following the steps outlined above, you should be able to find the rebound speed using the given graph.