A 50g tennis ball is thrown with a velocity of 12 m/s. It strikes a wall and rebounds with a velocity of 10 m/s.
a) What is the ball's initial and final momentum?
b) what is the impulse on the ball?
c) Thje ball is in contact with the wall for .10 second. with what force did the ball hit the wall?
Please show all work!
Sure! Let's go through each part of the question step by step:
a) To find the initial momentum of the ball, we need to multiply its mass by its velocity. The mass of the ball is given as 50g, which is equal to 0.05 kg (since 1 kg = 1000 g). The initial velocity of the ball is given as 12 m/s. Therefore, the initial momentum of the ball is:
Initial momentum = Mass × Velocity
= 0.05 kg × 12 m/s
= 0.6 kg·m/s
The final momentum of the ball can be calculated in the same way, using the mass and velocity after it rebounds. The final velocity is given as 10 m/s. Therefore, the final momentum is:
Final momentum = Mass × Velocity
= 0.05 kg × 10 m/s
= 0.5 kg·m/s
So, the ball's initial momentum is 0.6 kg·m/s and its final momentum is 0.5 kg·m/s.
b) Impulse is defined as the change in momentum. It can be calculated by subtracting the initial momentum from the final momentum. Therefore, the impulse on the ball is:
Impulse = Final momentum - Initial momentum
= 0.5 kg·m/s - 0.6 kg·m/s
= -0.1 kg·m/s
Note that the negative sign indicates a decrease in momentum.
c) To find the force with which the ball hits the wall, we can use the definition of impulse. Impulse is given by the equation:
Impulse = Force × Time
Rearranging this equation, we can solve for force:
Force = Impulse / Time
From part b, we found that the impulse on the ball is -0.1 kg·m/s. And the time of contact with the wall is given as 0.10 seconds. Plugging these values into the equation, we can calculate the force:
Force = -0.1 kg·m/s / 0.10 s
= -1 kg·m/s²
So the force with which the ball hits the wall is -1 kg·m/s². Again, the negative sign indicates that the force is in the opposite direction of the motion.
That's it! If you have any further questions, feel free to ask.