A tennis ball (mass 57.0 g) moves toward the player's racquet at 46.4 m/s. It is in contact with the racquet for 3.60 ms, after which it moves in the opposite direction at 49.8 m/s. What is the average force on the ball due to the racquet? (Assume the ball is moving in the positive direction after the contact with the racquet. Indicate the direction with the sign of your answer.)
force*time=mass(Vf-Vi)=mass(49.8+46.4)
figure force, it is in the direction of the final velocity, positive
To find the average force on the ball due to the racquet, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
First, let's find the initial momentum of the ball before it comes in contact with the racquet. The momentum is given by the product of mass and velocity:
Initial Momentum (before contact) = mass * velocity = 0.057 kg * 46.4 m/s = 2.6848 kg·m/s
Next, let's find the final momentum of the ball after it moves in the opposite direction:
Final Momentum (after contact) = mass * velocity = 0.057 kg * (-49.8 m/s) = -2.8386 kg·m/s
The change in momentum is the difference between the final and initial momentum:
Change in Momentum = Final Momentum - Initial Momentum
= (-2.8386 kg·m/s) - (2.6848 kg·m/s)
= -5.5234 kg·m/s
Since the time is given in milliseconds, we need to convert it to seconds:
Contact Time = 3.60 ms = 3.60 × 10^(-3) s
Finally, we can calculate the average force using the formula:
Average Force = Change in Momentum / Contact Time
Substituting the values:
Average Force = (-5.5234 kg·m/s) / (3.60 × 10^(-3) s)
= -1534.8 N
Therefore, the average force on the ball due to the racquet is -1534.8 N, where the negative sign indicates the force is in the opposite direction to the initial velocity of the ball.