A tennis ball has a mass of 58 g. The ball is dropped from rest from a height of 1.8 m above the ground and falls vertically. The ball rebounds vertically to a height of 1.1 m. The effect of air resistance is negligible. What is the change in momentum of the ball during its collision with the ground?

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A tennis ball has a mass of 58 g - AQA - A-Level Physics - Question 26 - 2022 - Paper 1

Question 26

A tennis ball has a mass of 58 g. The ball is dropped from rest from a height of 1.8 m above the ground and falls vertically. The ball rebounds vertically to a heigh... show full transcript

Worked Solution & Example Answer:A tennis ball has a mass of 58 g - AQA - A-Level Physics - Question 26 - 2022 - Paper 1

Step 1

Calculate the initial momentum before impact

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Answer

The momentum of the ball just before impact can be calculated using the formula:

$p = mv$

First, we need to find the velocity just before it hits the ground. We can use the formula for free fall:

$v = heta + ext{sqrt}(2gh)$

where:

$g \approx 9.81 \, m/s^2$ (acceleration due to gravity)
$h = 1.8 \, m$ (height of drop)

Substituting the values:

$v = ext{sqrt}(2 \times 9.81 \times 1.8) \approx 5.93 \, m/s$

Now, converting mass from grams to kilograms:

$m = 58 \, g = 0.058 \, kg$

Thus, the initial momentum is:

$p = 0.058 \times 5.93 \approx 0.34434 \, kg \, m/s$

Step 2

Calculate the final momentum after rebounding

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Answer

Next, we calculate the momentum of the ball after it rebounds to a height of 1.1 m. Using the same formula for free fall:

$v_{final} = \text{sqrt}(2gh)$

where $h = 1.1 \, m$ :

$v_{final} = \text{sqrt}(2 \times 9.81 \times 1.1) \approx 4.69 \, m/s$

The final momentum is then:

$p_{final} = 0.058 \times 4.69 \approx 0.27262 \, kg \, m/s$

Step 3

Calculate the change in momentum

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Answer

The change in momentum during the collision with the ground can be calculated as:

$\Delta p = p_{final} - (-p_{initial}) = p_{final} + p_{initial}$

Substituting the calculated values:

$\Delta p = 0.27262 + 0.34434 = 0.61696 \, kg \, m/s$

Thus, the change in momentum is approximately:

$\Delta p \approx 0.617 \, N \, s$

Step 4

Select the closest option

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Answer

Comparing with the options provided:

A. 0.040 N s
B. 0.075 N s
C. 0.215 N s
D. 0.614 N s

The closest option is D. 0.614 N s.

A tennis ball has a mass of 58 g - AQA - A-Level Physics - Question 26 - 2022 - Paper 1

Worked Solution & Example Answer:A tennis ball has a mass of 58 g - AQA - A-Level Physics - Question 26 - 2022 - Paper 1

Calculate the initial momentum before impact

Calculate the final momentum after rebounding

Calculate the change in momentum

Select the closest option

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