A tennis ball with mass 57 g is travelling at 45 m/s [S] when it is intercepted by a tennis racquet that applies an average force of 200 N during a short period of time, after which the ball travels at 62 m/s [N]. What is the time of contact between the ball and the racquet?
let t equal time of contact
change in velocity is ... 62 m/s + 45 m/s = 107 m/s
acceleration is ... (107 m/s) / t
f = m a ... 200 N = .057 kg * 107 m/s / t
200 t = .057 * 107
To find the time of contact between the ball and the racquet, we can use the impulse-momentum equation:
Impulse = Change in momentum
The impulse (J) is equal to the force (F) multiplied by the time (Δt):
J = F * Δt
And the change in momentum (Δp) is equal to the mass (m) multiplied by the change in velocity (Δv):
Δp = m * Δv
Given:
Mass of the ball (m) = 57 g = 0.057 kg
Initial velocity (v1) = 45 m/s [S]
Final velocity (v2) = 62 m/s [N]
Force applied (F) = 200 N
First, we need to find the change in velocity:
Δv = v2 - v1
Δv = 62 m/s - 45 m/s
Δv = 17 m/s
Now, we can calculate the change in momentum:
Δp = m * Δv
Δp = 0.057 kg * 17 m/s
Δp = 0.969 kg⋅m/s
Finally, we can find the time of contact using the impulse-momentum equation:
J = F * Δt
0.969 kg⋅m/s = 200 N * Δt
Rearranging the equation to solve for Δt:
Δt = (0.969 kg⋅m/s) / (200 N)
Δt ≈ 0.00485 s
Therefore, the time of contact between the ball and the racquet is approximately 0.00485 seconds.
To find the time of contact between the ball and the racquet, you can use the equation:
force = (change in momentum) / (time of contact)
First, let's calculate the change in momentum of the tennis ball using the equation:
change in momentum = mass * (final velocity - initial velocity)
Given:
Mass of the tennis ball (m) = 57 g = 0.057 kg
Initial velocity (u) = 45 m/s [S]
Final velocity (v) = 62 m/s [N]
Change in momentum = 0.057 kg * (62 m/s - 45 m/s)
Next, we can calculate the force using the equation:
force = 200 N
Now, we can rearrange the equation to solve for the time of contact:
time of contact = (change in momentum) / force
Substituting the given values:
time of contact = (0.057 kg * (62 m/s - 45 m/s)) / 200 N
Simplifying this equation will give you the time of contact between the ball and the racket.