Hi,
I honestly don't know how to approach this question and what equation to use.
A 50.0 g Super Ball traveling at 28.0 m/s bounces off a brick wall and rebounds at 18.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average acceleration of the ball during this time interval? (Note: 1 ms = 10-3 s.)
Can anyone help me? What equation would I use and would I use -g or a +g?
Thanks in advance.
accelerlation is change of velocity/time
= (vf-vi)/time
Now for the details. Let the direction of vi be positive, so vf is negative.
= (-18-28)/time watch the units of time.
Force = rate of change of momentum
= (momentum out - momentum in)/time
momentum out = -50*10^-3*18 kg m/s
momentum in = +50*10^-3*28
momentum out - momentum in = -50*10^-3*46
Force = -50*10^-3*46/3.5*10^-3 s
acceleration = Force/mass = -46/3.5*10^-3
= -13.1*10^3 = 1.31*10^4 m/s^2
To find the magnitude of the average acceleration of the ball during the contact with the wall, you can use the equation:
acceleration = (change in velocity) / (change in time)
In this case, since you are given the initial velocity (vi = 28.0 m/s), final velocity (vf = 18.0 m/s), and the time of contact (t = 3.50 ms = 3.50 × 10^-3 s), you can calculate the change in velocity as:
change in velocity = vf - vi
Now, let's calculate it:
change in velocity = 18.0 m/s - 28.0 m/s
= -10.0 m/s
The negative sign indicates that the direction of the velocity has changed. This means that the ball rebounded in the opposite direction.
Next, we need to convert the time from milliseconds (ms) to seconds (s). You can do this by dividing the time by 1000:
change in time = 3.50 × 10^-3 s / 1000
= 3.50 × 10^-6 s
Now, we can substitute the values into the equation to find the average acceleration:
acceleration = (change in velocity) / (change in time)
= (-10.0 m/s) / (3.50 × 10^-6 s)
Calculating:
acceleration = -2.86 × 10^6 m/s²
As for the sign, it depends on the coordinate system you choose. In this case, the acceleration is negative because the ball is slowing down as it rebounds. However, if you want to consider positive acceleration as upwards, you could consider using -g as acceleration due to gravity. But bear in mind that the question doesn't provide any information about the direction of gravity, so you should assume it as positive according to the standard convention.