In a typical golf swing, the club is in contact with the ball for about 0.0010s.
If the 45-g ball acquires a speed of 41 m/s, estimate the magnitude of the force exerted by the club on the ball.
a = (Vf - Vo) /t,
a = (41 - 0) / 0.0010 = 41000m/s^2.
F = ma = 0.045 * 41000 = 1845N.
To estimate the magnitude of the force exerted by the club on the ball, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the force applied to it multiplied by the time over which the force is exerted.
The change in momentum of the ball can be calculated as the difference between its final momentum and initial momentum. The initial momentum can be calculated using the mass of the ball and its initial velocity, assuming it starts from rest. The final momentum can be calculated using the mass of the ball and its final velocity.
The equation for the change in momentum is:
Δp = p_final - p_initial
The equation for momentum is:
p = m * v
Where:
Δp is the change in momentum
p_final is the final momentum
p_initial is the initial momentum
m is the mass of the ball
v is the velocity of the ball
Given that the mass of the ball is 45 grams, we first convert it to kilograms:
m = 45 g = 0.045 kg
The initial velocity is assumed to be 0 m/s since the ball starts from rest.
The final velocity of the ball is given as 41 m/s.
Now we can calculate the initial momentum and final momentum:
p_initial = m * v_initial = 0.045 kg * 0 m/s = 0 kg·m/s
p_final = m * v_final = 0.045 kg * 41 m/s = 1.845 kg·m/s
The change in momentum is:
Δp = p_final - p_initial = 1.845 kg·m/s - 0 kg·m/s = 1.845 kg·m/s
Now, to estimate the magnitude of the force applied by the club, we need to divide the change in momentum by the time of contact between the club and the ball.
Given that the contact time is approximately 0.0010 s, we can calculate the force using the formula:
F = Δp / Δt
Where:
F is the force exerted by the club on the ball
Δp is the change in momentum
Δt is the time of contact
Substituting the values, we get:
F = 1.845 kg·m/s / 0.0010 s = 1845 N
Therefore, the estimated magnitude of the force exerted by the club on the ball is approximately 1845 Newtons.