A .060kg tennis ball crosses the net a 40m/s and is returned back across the net at 36m/s by the other player. If the contact time between racket and the ball is .0250s, what is the average force on the ball?
Δp = F•Δt,
Δp = p2 - p1 =m•v1 - m• (-v2) =
= m• (v1+v2),
F•Δt = m• (v1+v2),
F = m•(v1+v2)/ Δt = 0.06(40+36)/0.025=
= 182.4 N.
To find the average force on the tennis ball, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it.
Let's break down the problem step by step:
Step 1: Calculate the initial momentum of the ball.
The initial momentum of the ball can be found using the formula: momentum = mass * velocity.
Given: mass of the ball (m) = 0.060 kg, initial velocity (v1) = 40 m/s.
So, initial momentum (p1) = m * v1.
Step 2: Calculate the final momentum of the ball.
The final momentum of the ball can be found using the same formula: momentum = mass * velocity.
Given: mass of the ball (m) = 0.060 kg, final velocity (v2) = -36 m/s (negative because it's in the opposite direction).
So, final momentum (p2) = m * v2.
Note: The negative sign in front of the final velocity indicates that the direction of the ball is opposite to its initial direction.
Step 3: Calculate the change in momentum.
The change in momentum can be found by subtracting the final momentum (p2) from the initial momentum (p1).
Change in momentum (Δp) = p2 - p1.
Step 4: Calculate the average force.
The average force can be found using the equation: average force (F) = Δp / Δt.
Given: contact time (Δt) = 0.0250 s.
So, average force (F) = Δp / Δt.
Let's plug in the values and calculate:
p1 = (0.060 kg) * (40 m/s)
p2 = (0.060 kg) * (-36 m/s)
Δp = p2 - p1
F = Δp / Δt
Now, we can substitute the values into the formula and calculate the average force.