In a typical golf swing, the club is in contact with the ball for about 0.0010 .
If the 45- ball acquires a speed of 57 , estimate the magnitude of the force exerted by the club on the ball.
units?
To estimate the magnitude of the force exerted by the club on the ball, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In this case, we need to calculate the acceleration of the ball.
Given:
Time of contact (t) = 0.0010 s
Initial velocity (v) = 0 (assuming the ball starts from rest)
Final velocity (u) = 57 m/s
We can use the equation v = u + at to calculate the acceleration (a), and then use F = ma to find the force (F).
Rearranging the equation v = u + at to solve for a:
a = (v - u) / t
Plugging in the given values:
a = (57 m/s - 0 m/s) / 0.0010 s
a = 57,000 m/s^2
Now, we can calculate the force (F) using F = ma:
F = (mass of the ball) * (acceleration)
The mass of a golf ball is usually around 45 grams. However, we need to convert it to kilograms by dividing by 1000:
Mass (m) = 45 g / 1000 = 0.045 kg
F = 0.045 kg * 57,000 m/s^2
F ≈ 2,565 N
Therefore, the magnitude of the force exerted by the club on the ball is approximately 2,565 Newtons.