A high-speed photograph of a club hitting a golf ball is shown in the figure below. The club was in contact with a ball, initially at rest, for about 0.0049 s. If the ball has a mass of 55 g and leaves the head of the club with a speed of 2.1 102 km/h, find the average force exerted on the ball by the club.
force * time = change in momentum = m v
To find the average force exerted on the ball by the club, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration.
First, let's convert the speed of the ball from km/h to m/s.
1 km/h = 1000 m/3600 s ≈ 0.2778 m/s
So, the speed of the ball is 2.1 * 10^2 km/h * 0.2778 m/s = 0.58333 * 10^2 m/s = 58.333 m/s (approx).
Next, let's calculate the acceleration of the ball.
Acceleration is the change in velocity divided by the time it takes for the change to occur. Since the ball starts from rest, its initial velocity is 0 m/s.
Change in velocity = final velocity - initial velocity = 58.333 m/s - 0 m/s = 58.333 m/s
The time taken for the change in velocity is given as 0.0049 s.
Acceleration = change in velocity / time taken = (58.333 m/s) / (0.0049 s) = 11906.122 m/s^2 (approx)
Now, we can find the force exerted on the ball using Newton's second law.
Force = mass * acceleration
The mass of the ball is given as 55 g. We need to convert it to kg.
1 g = 0.001 kg
So, the mass of the ball is 55 g * 0.001 kg/g = 0.055 kg.
Force = 0.055 kg * 11906.122 m/s^2 ≈ 655.86 N
Therefore, the average force exerted on the ball by the club is approximately 655.86 N.
To find the average force exerted on the ball by the club, we can use the equation:
Average Force = (Change in Momentum) / (Time)
The change in momentum can be calculated using the equation:
Change in Momentum = Final Momentum - Initial Momentum
The final momentum of the ball can be calculated using the equation:
Final Momentum = Mass * Final Velocity
Given:
Mass of the ball (m) = 55 g = 0.055 kg
Final Velocity (v) = 2.1 * 10^2 km/h = 2.1 * 10^2 * 1000 m/3600 s (converting km/h to m/s)
Time (t) = 0.0049 s
Calculating the final velocity:
Final Velocity = 2.1 * 10^2 * 1000 m/3600 s
= 5.83 m/s (rounded to two decimal places)
Calculating the final momentum:
Final Momentum = Mass * Final Velocity
= 0.055 kg * 5.83 m/s
= 0.319 kg.m/s (rounded to three decimal places)
The initial momentum of the ball is zero since it was initially at rest.
Calculating the change in momentum:
Change in Momentum = Final Momentum - Initial Momentum
= 0.319 kg.m/s - 0 kg.m/s
= 0.319 kg.m/s (rounded to three decimal places)
Now, we can calculate the average force exerted on the ball:
Average Force = Change in Momentum / Time
= 0.319 kg.m/s / 0.0049 s
= 65.1 N (rounded to one decimal place)
Therefore, the average force exerted on the ball by the club is 65.1 N.