a child bounces a superball on the sidewalk. The velocity change of the superball is from 23m/s downward to 14m/s upward. if the contact time with the sidewalk is 1/800s, what is the magnitude of the average force exerted on the superball by the sidewalk?
List the formulas your teacher has you use, so I can solve it using methods that you are familiar with.
To calculate the magnitude of the average force exerted on the superball by the sidewalk, we can make use of Newton's second law of motion: force equals mass times acceleration (F = ma). In this case, we know the velocity change of the superball (from 23m/s downward to 14m/s upward) and the contact time with the sidewalk (1/800s).
First, we need to determine the acceleration of the superball during the contact time. We can use the formula for average acceleration: a = (final velocity - initial velocity) / time.
Given:
Initial velocity, u = 23 m/s downward
Final velocity, v = 14 m/s upward
Contact time, t = 1/800 s
So, the acceleration, a = (14 - (-23)) / (1/800) = 37 / (1/800) = 37 * (800/1) = 37 * 800 m/s².
Now, we know the acceleration. To find the magnitude of the average force, we need to know the mass of the superball. However, this information is not provided in the question. To proceed, we will make use of the impulse-momentum relationship.
Impulse (J) is defined as the product of force and time (J = Ft), and momentum (p) is defined as the product of mass and velocity (p = mv). In this case, we can assume that the mass of the superball remains constant throughout the interaction with the sidewalk.
During the contact time, the change in momentum of the superball is given by:
Δp = mΔv = m(v - u)
Since the time duration is very short, we assume that the net force is constant and use the average force formula:
F_ave = Δp / t
Substituting the values:
F_ave = (m(v - u)) / t
Without knowing the mass of the superball, we cannot find the exact value of the force exerted by the sidewalk.