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A golf ball has a mass of 46 g and is initially stationary - AQA - A-Level Physics - Question 25 - 2021 - Paper 1

Question 25

A golf ball has a mass of 46 g and is initially stationary. The diagram shows the variation with time of the force acting on the golf ball as it is hit with a golf c... show full transcript

Worked Solution & Example Answer:A golf ball has a mass of 46 g and is initially stationary - AQA - A-Level Physics - Question 25 - 2021 - Paper 1

Step 1

Calculate the average force

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Answer

To estimate the kinetic energy, we first determine the average force applied to the golf ball during the time interval. From the provided graph, the peak force reaches approximately 0.7 kN. The average force can be estimated by considering the area under the force-time graph. Given that the graph rises and falls, we can approximate this area as a triangle to find the average force over the first part of the impact time.

Step 2

Estimate the change in momentum

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Answer

The impulse imparted to the golf ball is equal to the average force multiplied by the time interval during which the force acts. If we assume the time interval is roughly 10 ms (0.01 s), we can calculate the impulse:

$Impulse = F_{avg} \times \Delta t$

where ( F_{avg} \approx \rac{0.7 ext{ kN}}{2} = 0.35 ext{ kN} = 350 ext{ N} $and \( \Delta t = 0.01 s$ , yielding

$Impulse \approx 350 ext{ N} \times 0.01 s = 3.5 ext{ N s}$ .

Step 3

Calculate the final velocity

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Answer

The impulse also equals the change in momentum:

$Impulse = m \times v$ where ( m = 0.046 ext{ kg} ). Thus, we can find the final velocity ( v ):

$3.5 = 0.046 v \Rightarrow v \approx \frac{3.5}{0.046} \approx 76.09 ext{ m/s}$ .

Step 4

Calculate the kinetic energy

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Answer

Finally, we calculate the kinetic energy (KE) of the golf ball using the formula:

$KE = \frac{1}{2}mv^2$ . Substituting the values we found, we have:

$KE \approx \frac{1}{2} \times 0.046 \times (76.09)^2 \approx 107.70 ext{ J}.$
Thus, the estimated kinetic energy is closest to option C) 250 J.

A golf ball has a mass of 46 g and is initially stationary - AQA - A-Level Physics - Question 25 - 2021 - Paper 1

Worked Solution & Example Answer:A golf ball has a mass of 46 g and is initially stationary - AQA - A-Level Physics - Question 25 - 2021 - Paper 1

Calculate the average force

Estimate the change in momentum

Calculate the final velocity

Calculate the kinetic energy

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