Final answer:
To calculate the force a tennis ball exerts on a wall, you sum its initial and final velocities to find the change in velocity, multiply it by the ball's mass to find the change in momentum, and then divide by the time of contact to find the force. The force is found to be 198.57 N.
Step-by-step explanation:
A tennis ball is flying eastward towards a wall with a speed of 43.4 m/s. After bouncing against the wall, it's flying westward with a speed of 26.1 m/s. Given that the mass of the ball is 0.1 kg and the time the tennis ball is in contact with the wall is 0.035 s, we can calculate the magnitude of the force the ball exerts on the wall.
Step-by-Step Explanation
- Calculate the change in velocity (\(\Delta v\)). The initial velocity is 43.4 m/s eastward and the final velocity is 26.1 m/s westward. Since they're in opposite directions, we add them to get the total change: \(\Delta v = 43.4 m/s + 26.1 m/s = 69.5 m/s\).
- Find the change in momentum (\(\Delta p\)). Since \(\Delta p = m \times \Delta v\), plug in the mass (0.1 kg) and the change in velocity (69.5 m/s): \(\Delta p = 0.1 kg \times 69.5 m/s = 6.95 kg\cdot m/s\).
- Calculate the force (\(F\)) using the impulse equation \(F \times \Delta t = \Delta p\), where \(\Delta t\) is the time interval (0.035 s): \(F = \Delta p / \Delta t = 6.95 kg\cdot m/s / 0.035 s\).
- After calculating the force, we find that the magnitude of the force the ball exerts on the wall is 198.57 N.