In a typical golf swing, the club is in contact with the ball for about 0.0015 s. If the 45 g ball acquires a speed of 75 m/s, estimate the magnitude of the force exerted by the club on the ball.
force*time=massball*changevelocity
67000
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 (F) is equal to the change in momentum (p) divided by the time interval (Δt) over which the change occurs. Mathematically, it can be expressed as:
F = Δp / Δt
In this case, we know that the ball acquires a speed of 75 m/s, and its mass (m) is 45 g. To find the change in momentum (Δp), we can multiply the mass by the change in velocity (Δv):
Δp = m * Δv
Here, Δv is the change in velocity, which can be calculated as the final velocity (vf) minus the initial velocity (vi). In this case, the ball starts from rest, so the initial velocity (vi) is 0 m/s. Therefore:
Δv = vf - vi = 75 m/s - 0 m/s = 75 m/s
Substituting the values into the equation, we get:
Δp = (0.045 kg) * (75 m/s) = 3.375 kg·m/s
Now, we need to consider the time interval (Δt) over which the change in momentum occurs. It is given in the question that the club is in contact with the ball for about 0.0015 s.
Substituting the values into the equation, we get:
Δt = 0.0015 s
Finally, we can calculate the magnitude of the force (F) using Newton's second law:
F = Δp / Δt = (3.375 kg·m/s) / (0.0015 s) = 2250 N
Therefore, the estimated magnitude of the force exerted by the club on the ball is 2250 Newtons.