To find the average force exerted on the ball by the club, we can use the following steps:

Step 1: Calculate the change in momentum (Impulse)

Impulse is the product of the average force $F_{\text{avg}}$ and the time duration $t$ of the contact:

$\text{Impulse} = F_{\text{avg}} \cdot t$

Impulse is also equal to the change in momentum:

$\text{Impulse} = \Delta p = m \cdot \Delta v$

Where:

• $m$ is the mass of the ball (in kg),
• $\Delta v$ is the change in velocity (since the ball starts at rest, this is just the final velocity),
• $t$ is the time of contact (in seconds).

Step 2: Convert units

First, we need to convert the mass and velocity into consistent units:

1. Mass: The ball’s mass is given as 55 g. To convert to kilograms: $m = 55 \, \text{g} = 55 \times 10^{-3} \, \text{kg} = 0.055 \, \text{kg}$

2. Velocity: The ball’s final speed is $2.5 \times 10^2 \, \text{ft/s}$. To convert to meters per second: $v = 2.5 \times 10^2 \, \text{ft/s} = 2.5 \times 10^2 \times 0.3048 \, \text{m/s} = 76.2 \, \text{m/s}$

3. Time: The time of contact is already given as $t = 0.0052 \, \text{s}$.

Step 3: Calculate the change in momentum

Since the initial velocity is zero (the ball starts at rest):

$\Delta v = v - 0 = 76.2 \, \text{m/s}$

Now calculate the change in momentum:

$\Delta p = m \cdot \Delta v = 0.055 \, \text{kg} \cdot 76.2 \, \text{m/s} = 4.191 \, \text{kg} \cdot \text{m/s}$

Step 4: Find the average force

From the impulse-momentum relationship:

$F_{\text{avg}} = \frac{\Delta p}{t} = \frac{4.191 \, \text{kg} \cdot \text{m/s}}{0.0052 \, \text{s}} = 806.73 \, \text{N}$

Step 5: Convert to kilonewtons

To convert the force to kilonewtons (kN):

$F_{\text{avg}} = 806.73 \, \text{N} \div 1000 = 0.807 \, \text{kN}$

Final Answer:

The average force exerted on the ball by the club is approximately 0.807 kN.

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Would you like more details on any part of the solution, or do you have any questions about the process?

Here are some related questions for further exploration:

1. How would the result change if the ball had a greater mass or if it was in contact with the club for a longer time?
2. How is impulse related to the concept of momentum?
3. What would happen if the ball had been launched at an angle instead of horizontally?
4. How does the velocity of the ball affect the impact force?
5. How do you calculate the velocity of an object after an impulse is applied over a specific time?

Tip: When dealing with problems involving forces, always ensure your units are consistent. Converting mass to kilograms and velocity to meters per second helps in using the SI unit system and avoids errors.