when a tennis ball is served, it is a contact with the racket for a time that is typical 0.005 seconds. find the force needed to serve a 60.0 gram tennis ball moving with a velocity of 30.0m/s
change in momentum = 0.060 kg * 30 m/s
time = 0.005 seconds
force = change in momentum/ time
To find the force needed to serve a tennis ball, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, the acceleration during contact between the racket and ball is what we need to determine.
First, let's find the acceleration. We know that acceleration can be calculated by dividing the change in velocity (Δv) by the time it takes for that change (Δt). In this case, the initial velocity (v_i) is zero since the ball is at rest before being served, and the final velocity (v_f) is 30.0 m/s.
Δv = v_f - v_i
Δv = 30.0 m/s - 0 m/s
Δv = 30.0 m/s
Next, we need to find the time (Δt) by converting the given time into seconds.
Given time = 0.005 seconds
Now, let's substitute the values into the acceleration formula:
a = Δv / Δt
a = 30.0 m/s / 0.005 s
a = 6000 m/s²
With the acceleration determined, we can now calculate the force using Newton's second law:
F = m * a
F = 60.0 g * 0.001 kg/g * 6000 m/s²
F = 3.6 kg * 6000 m/s²
F = 21,600 N
Therefore, the force needed to serve a 60.0 gram tennis ball moving with a velocity of 30.0 m/s is 21,600 Newtons.