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 momentum just before hitting the ground

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Answer

First, we will convert the mass of the tennis ball from grams to kilograms: 58 g = 0.058 kg.

Next, we calculate the velocity of the ball just before it hits the ground using the formula for gravitational potential energy and kinetic energy:

Potential energy at height 1.8 m is converted to kinetic energy just before impact:

$PE = mgh = 0.058 imes 9.81 imes 1.8$

Solving for the velocity, we use:

$v = ext{sqrt}(2gh) = ext{sqrt}(2 imes 9.81 imes 1.8)$

Substituting the values, we get: $v \approx 5.88 ext{ m/s}.$

Thus, the momentum just before hitting the ground is: $$p = mv = 0.058 \times 5.88 = 0.341 ext{ kg m/s}.$

Step 2

Calculate the momentum just after rebounding

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Now, we calculate the momentum of the ball just after rebounding to a height of 1.1 m:

Similarly, the velocity just after rebounding can be calculated using: $v' = ext{sqrt}(2gh') = ext{sqrt}(2 \times 9.81 \times 1.1)$

Substituting the values, we find: $v' \approx 4.67 ext{ m/s}.$

Thus, the momentum just after rebounding is: $$p' = mv' = 0.058 \times 4.67 = 0.271 ext{ kg m/s}.$

Step 3

Calculate the change in momentum

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Finally, the change in momentum ( Δp) during the collision is calculatedas:

$\Delta p = p' - (-p) = 0.271 - (-0.341) = 0.271 + 0.341 = 0.612 ext{ kg m/s}.$

Thus, the change in momentum of the ball during its collision with the ground is approximately 0.614 N s.

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Questions answered

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 momentum just before hitting the ground

Calculate the momentum just after rebounding

Calculate the change in momentum

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