A rubber ball is thrown against the wall. The ball has a mass of 4 g and strikes the wall perpendicularly with a speed of 12 m/s. The acceleration is constant while the ball is touching the wall. After touching the wall, the center of mass moves .5 cm toward the wall, and back out from the wall.
what is the magnitude of the time average force?
>>First I found the impulse delivered by the wall which is Px'-Px (momentum) = .096 N/s. Then I tried to find the change in time by taking (.5*2*(1/1000))/12. For this change in time i got 8.33E-4. However, the answer .096/8.33E-4 was incorrect. Help!
The average velocity from first impact to turnaround (maximum compression) is 6 m/s. The time required to reach maximum compression (at constant acceleration) is T = 0.5 cm/(600 cm/s)= 8.3*10^-4 s. Acceleration is
a = (delta V)/T
a = (12 m/s)/(8.3*10^-4s) = 14,400 m/s^2
M = m a = (0.004 kg)(14,400 m/s^2) = 57.6 N
I understand how you got the impulse. The units of momentum are not N/s. The time agrees with mine, but mine is half the total interval of contact, and yours is the total time of contact. Something is wrong there
To find the magnitude of the time average force, let's break down the problem step by step.
Step 1: Calculate the impulse delivered by the wall.
Impulse can be calculated as the change in momentum. In this case, the change in momentum can be determined by the formula:
Impulse = Px' - Px,
where Px is the initial momentum and Px' is the final momentum.
Given that the ball has a mass of 4 g (which is 0.004 kg) and a speed of 12 m/s, we can calculate the initial momentum Px as:
Px = m * v = 0.004 kg * 12 m/s = 0.048 kg·m/s.
Next, we need to determine the final momentum. The problem states that the center of mass moves 0.5 cm toward the wall and back out after touching it. This implies that the velocity of the ball changes sign during this motion, and thus, the final momentum is the negative of the initial momentum:
Px' = -Px = -0.048 kg·m/s.
The impulse delivered by the wall can now be calculated as the difference between the initial and final momentum:
Impulse = Px' - Px = (-0.048 kg·m/s) - (0.048 kg·m/s) = -0.096 kg·m/s.
Step 2: Calculate the duration of the collision.
To find the duration of the collision, we can calculate the change in time. The problem gives a displacement of 0.5 cm (which is 0.005 m) and asks for the change in time. To find this, we can apply the formula:
Δt = 2Δx / v,
where Δx is the displacement and v is the velocity of the ball.
Plugging in the values, we get:
Δt = (2 * 0.005 m) / 12 m/s = 0.000833 s.
Now we have the duration of the collision.
Step 3: Calculate the magnitude of the time average force.
The magnitude of the time average force can be found using the equation:
Magnitude of time average force = Impulse / Δt.
Plugging in the calculated values, we have:
Magnitude of time average force = (-0.096 kg·m/s) / 0.000833 s ≈ -115.28 N.
Note that the negative sign indicates that the force is exerted by the wall on the ball in the opposite direction of the ball's initial motion.
So, the magnitude of the time average force exerted by the wall on the ball is approximately 115.28 N.