A child bounces a 55 g superball on the side-
walk. The velocity change of the superball is
from 22 m/s downward to 14 m/s upward.
If the contact time with the sidewalk is
1
800
s, what is the magnitude of the average force
exerted on the superball by the sidewalk? Answer in units of N
yes
To find the magnitude of the average force exerted on the superball by the sidewalk, you can use the impulse-momentum equation:
Impulse = Change in momentum
The impulse is given by the formula:
Impulse = Force * Time
And the change in momentum is given by:
Change in momentum = Mass * (Final Velocity - Initial Velocity)
Given:
Mass of the superball (m) = 55 g = 0.055 kg
Initial velocity (u) = 22 m/s downward
Final velocity (v) = 14 m/s upward
Contact time (t) = 1,800 s
Let's calculate the change in momentum first:
Change in momentum = 0.055 kg * (14 m/s - (-22 m/s))
= 0.055 kg * (14 m/s + 22 m/s)
= 0.055 kg * 36 m/s
= 1.98 kg⋅m/s
Now, we can use the impulse-momentum equation to find the average force:
Impulse = Force * Time
1.98 kg⋅m/s = Force * 1,800 s
Rearranging the equation to solve for the force:
Force = Impulse / Time
= 1.98 kg⋅m/s / 1,800 s
Calculating the magnitude of the average force:
Force = 1.1 N
Therefore, the magnitude of the average force exerted on the superball by the sidewalk is 1.1 N.
To find the magnitude of the average force exerted on the superball by the sidewalk, we can use the impulse-momentum principle. The impulse experienced by an object is equal to the change in its momentum. In equation form, this principle can be written as:
Impulse = Change in momentum
The impulse is given by the product of the average force and the contact time:
Impulse = Average force * Contact time
The momentum change of the superball can be calculated by subtracting the initial momentum from the final momentum:
Momentum change = Final momentum - Initial momentum
The mass of the superball is 55 g, which is equal to 0.055 kg in SI units. The final momentum can be calculated by multiplying the final velocity by the mass, and the initial momentum is obtained by multiplying the initial velocity by the mass.
So, let's calculate the magnitude of the average force exerted on the superball by the sidewalk step by step:
Step 1: Convert the mass of the superball to kilograms:
Mass = 55 g = 0.055 kg
Step 2: Calculate the momentum change:
Momentum change = (Final momentum) - (Initial momentum)
= (Final velocity * Mass) - (Initial velocity * Mass)
= (14 m/s * 0.055 kg) - (22 m/s * 0.055 kg)
Step 3: Calculate the impulse using the relation:
Impulse = Average force * Contact time
Step 4: Rearrange the impulse formula to solve for the average force:
Average force = Impulse / Contact time
Step 5: Substitute the values to find the average force:
Average force = (Momentum change) / (Contact time)
Now, plug in the values mentioned in the problem:
Average force = (14 m/s * 0.055 kg - 22 m/s * 0.055 kg) / (1/800 s)
After performing the calculation, you will find the magnitude of the average force exerted on the superball by the sidewalk in units of Newtons (N).
change velocity (Vf-Vi)= (14-(-22)=36m/s upward
force*timecontact= mass*changevelocity
solve for force.