a 0.2kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30 m/s and rebounds up at 25 m/s. If the ball is in contact with the sidewalk for 0.025s, what is the magnitude of the average force applied by the sidewalk on the ball?
I need steps on how to do this including equations ASAP!
Well, let's first calculate the change in momentum of the ball during the collision with the sidewalk.
The change in momentum (∆p) can be calculated using the equation:
∆p = m * ∆v
Where m is the mass of the ball and ∆v is the change in velocity. In this case, since the ball initially had a downward velocity of 30 m/s and then rebounded up with a velocity of 25 m/s, the change in velocity can be calculated as:
∆v = 25 m/s - (-30 m/s) = 55 m/s
Substituting the values into the equation:
∆p = 0.2 kg * 55 m/s = 11 kg·m/s
Now, the impulse (∆J) experienced by the ball during the collision can be calculated using the equation:
∆J = ∆p = F * ∆t
Where F is the average force applied by the sidewalk on the ball and ∆t is the duration of the collision. In this case, ∆t is given as 0.025 s.
Substituting the values into the equation:
11 kg·m/s = F * 0.025 s
To solve for the average force (F), we can rearrange the equation:
F = 11 kg·m/s / 0.025 s
Calculating the value:
F = 440 N
So, the magnitude of the average force applied by the sidewalk on the ball is 440 Newtons.
Now, I hope this answer isn't too hard to "bounce" off of!
To find the magnitude of the average force applied by the sidewalk on the ball, we can use the impulse-momentum principle.
Step 1: Determine the initial and final velocities of the ball.
- The initial velocity of the ball (v1) is 30 m/s (downward) as it strikes the sidewalk.
- The final velocity of the ball (v2) is 25 m/s (upward) as it rebounds.
Step 2: Calculate the change in velocity (∆v).
- ∆v = v2 - v1
- ∆v = 25 m/s - (-30 m/s)
- ∆v = 55 m/s
Step 3: Calculate the impulse (J) using the formula:
- J = m * ∆v
- where m is the mass of the ball, which is 0.2 kg.
Substituting the values:
- J = 0.2 kg * 55 m/s
- J = 11 Ns
Step 4: Calculate the average force (F_avg) using the formula:
- F_avg = J / ∆t
- where ∆t is the time the ball is in contact with the sidewalk, given as 0.025 s.
Substituting the values:
- F_avg = 11 Ns / 0.025 s
- F_avg = 440 N
Therefore, the magnitude of the average force applied by the sidewalk on the ball is 440 N.
To find the magnitude of the average force applied by the sidewalk on the ball, we can use the concept of impulse. Impulse is defined as the change in momentum of an object and is equal to the force applied multiplied by the time interval for which the force was applied.
Step 1: Calculate the momentum before the collision
The momentum before the collision is given by the product of the mass of the ball (m) and its velocity before the collision (v1):
p1 = m * v1
Step 2: Calculate the momentum after the collision
The momentum after the collision is given by the product of the mass of the ball (m) and its velocity after the collision (v2):
p2 = m * v2
Step 3: Calculate the change in momentum
The change in momentum (Δp) is the difference between the momentum after the collision and the momentum before the collision:
Δp = p2 - p1
Step 4: Calculate the average force
The average force (F_avg) can be found by dividing the change in momentum by the time interval for which the force was applied (Δt):
F_avg = Δp / Δt
Given:
Mass of the ball (m) = 0.2 kg
Velocity before the collision (v1) = 30 m/s
Velocity after the collision (v2) = -25 m/s (negative sign indicates opposite direction)
Time interval (Δt) = 0.025 s
Using the equations and values given above, we can now calculate the magnitude of the average force.
Step 5: Calculate momentum before the collision
p1 = (0.2 kg) * (30 m/s) = 6 kg m/s
Step 6: Calculate momentum after the collision
p2 = (0.2 kg) * (-25 m/s) = -5 kg m/s
Step 7: Calculate change in momentum
Δp = p2 - p1 = (-5 kg m/s) - (6 kg m/s) = -11 kg m/s
Step 8: Calculate average force
F_avg = Δp / Δt = (-11 kg m/s) / (0.025 s)
= -440 N
The magnitude of the average force applied by the sidewalk on the ball is 440 N.
a=V-Vo)/t = (-25-30)/0.025=2200m/s^2.
F = m*a = 0.2 * 2200 = 440 N.
Note: The velocity when leaving sidewalk is in opposite direction(neg.).