When serving, a tennis ball is almost motionless when it is slammed by the racquet. A force sensor in an experimental tennis racquet measures a force of 80 N during the impact with a 0.058 kg tennis ball. The
impact lasts for 0.04 seconds. If the ball was at rest initially, what is its speed after the impact with the racquet?
F•Δt=Δp=m•Δv= m(v-0)
v= F•Δt/m = 80•0.04/0.058=55.17 m/s
To find the speed of the tennis ball after the impact with the racquet, we can use the concept of impulse and momentum.
The impulse experienced by an object is equal to the change in momentum it undergoes. In this case, the impulse can be calculated using the equation:
Impulse = Force x Time
Given that the force during the impact is 80 N and the duration of the impact is 0.04 seconds, the impulse can be calculated as follows:
Impulse = 80 N x 0.04 s
Impulse = 3.2 N.s
The change in momentum of the tennis ball can be calculated using the equation:
Change in Momentum = Mass x Velocity
The initial velocity of the ball is zero since it was at rest initially. Therefore, the change in momentum is equal to the final momentum.
The impulse is also equal to the change in momentum, so we can equate the two in order to find the final momentum of the ball:
3.2 N.s = 0.058 kg x Velocity
Simplifying the equation, we can solve for the velocity of the ball:
Velocity = 3.2 N.s / 0.058 kg
Velocity ≈ 55.17 m/s
Therefore, the speed of the tennis ball after the impact with the racquet is approximately 55.17 m/s.