A child bounces a 48 g superball on the sidewalk.
The velocity change of the superball is
from 22 m/s downward to 19 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
To find the magnitude of the average force exerted on the superball by the sidewalk, we can use the impulse-momentum principle.
The impulse is given by the change in momentum of the ball, which is equal to the mass of the ball multiplied by the change in velocity:
Impulse = mass * change in velocity
The change in velocity is the final velocity minus the initial velocity:
Change in velocity = final velocity - initial velocity
Given:
Mass of the superball (m) = 48 g = 0.048 kg (since 1 kg = 1000 g)
Initial velocity (v1) = 22 m/s downward
Final velocity (v2) = 19 m/s upward
To find the change in velocity, we need to consider the direction. Since the initial velocity is downward and the final velocity is upward, the change in velocity will be the sum of the magnitudes:
Change in velocity = |v2| + |v1| = 19 m/s + 22 m/s = 41 m/s
Substituting the values into the equation for impulse:
Impulse = mass * change in velocity
Impulse = 0.048 kg * 41 m/s = 1.968 kg·m/s
The impulse is also equal to the average force (F) multiplied by the contact time (Δt):
Impulse = F * Δt
Rearranging the equation to solve for force:
F = Impulse / Δt
F = 1.968 kg·m/s / 1800 s = 0.00109 N
Therefore, the magnitude of the average force exerted on the superball by the sidewalk is approximately 0.00109 N.
To find the magnitude of the average force exerted on the superball by the sidewalk, we can use the principle of momentum change.
The momentum of an object is defined as the product of its mass and velocity. The change in momentum of the superball can be calculated by subtracting the initial momentum from the final momentum.
First, let's find the initial momentum of the superball. The mass of the superball is given as 48 grams, which is equivalent to 0.048 kg. The initial velocity is 22 m/s downward, so the initial momentum is given by:
Initial momentum = mass x initial velocity
Initial momentum = 0.048 kg x (-22 m/s) (Note: we consider downward direction as negative)
Initial momentum = -1.056 kg m/s
Next, let's find the final momentum of the superball. The final velocity is 19 m/s upward, so the final momentum is given by:
Final momentum = mass x final velocity
Final momentum = 0.048 kg x 19 m/s
Final momentum = 0.912 kg m/s
Now, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 0.912 kg m/s - (-1.056 kg m/s)
Change in momentum = 0.912 kg m/s + 1.056 kg m/s
Change in momentum = 1.968 kg m/s
According to the principle of momentum change, the change in momentum is equal to the impulse applied to the object. Impulse is defined as the product of average force and the contact time. We are given the contact time as 1800 s.
So, we can rearrange the formula to solve for the average force:
Average force = Change in momentum / Contact time
Average force = 1.968 kg m/s / 1800 s
Average force ≈ 0.00109333 N (rounded to five decimal places)
Therefore, the magnitude of the average force exerted on the superball by the sidewalk is approximately 0.0011 N.
t = (1/800)s.
V = Vo + a*t = 19.
22 + a*(1/800) = 19,
a/800 = -3,
a = -2400 m/s^2.
F = M*a = 0.048 * (-2400) = -115.2 N.
The negative sign means the force opposes the motion.
Correction: V = Vo + a*t = 19 - (-22).
-22 + a*(1/800) = 41.
a/800 = 63,
a = 50,400 m/s^2.
F = M*a = 0.048 * (50,400) = 2419 N.