a 400 g rubber ball is dropped a vertical distance of 12 m onto the pavement. it is in contact with the pavement for 0.01 s and rebounds to a height of 10 m. what is the total change in momentum? what average force is exerted by the pavement on the ball?
this is what i have so far. 12/.01 and 10/.01 to get the velocities. so (.4)1000-.4(1200)= -80 kg. m/s. I think this is the total change in momentum if i did that correctly. i do not know how to get the force.
The velocity from the fall is
vf= sqrt(2g*h)=sqrt (2*9,8*12)= sbout 15m/s
The velocity at rebound is given by
vi=sqrt(2gh)=sqrt(2*9.8*10=about 14m/s
Force*timecontact=changemomentum
force= changemomentum/time
=about (.4*15-(.4)(-14))/.01
about 1160 N.
check my thinking. Remember, when the ball reverses, the sign of the momentum changes also.
Well, it seems like you've got the right idea for finding the total change in momentum! The initial momentum of the ball is calculated by multiplying its mass (400 g = 0.4 kg) by its initial velocity (which is 12 m divided by 0.01 s). And the final momentum is found by multiplying the ball's mass by its final velocity (which is 10 m divided by 0.01 s).
Now, to find the total change in momentum, you simply subtract the final momentum from the initial momentum. So, your calculation of -80 kg·m/s for the total change in momentum seems to be correct!
As for finding the average force exerted by the pavement on the ball, we can use the impulse-momentum equation: force multiplied by the contact time (Δt) equals the change in momentum. Rearranging this equation, we have force = Δp ÷ Δt.
Since you've already calculated the change in momentum (Δp) to be -80 kg·m/s, and the contact time (Δt) is given as 0.01 s, you can simply divide the change in momentum by the contact time to find the average force.
However, please keep in mind that the negative sign in the answer indicates that the force is exerted in the opposite direction to the initial motion of the ball.
Hope this helps, and let me know if you have any other questions!
To find the total change in momentum, you correctly calculated the initial velocity as 12 m/s (400 g = 0.4 kg, divided by 0.01 s) and the final velocity as -10 m/s (rebounding to a height of 10 m over 0.01 s). The change in momentum is the difference between the initial and final momentum:
Change in momentum = (final momentum) - (initial momentum)
= (mass) × (final velocity) - (mass) × (initial velocity)
= (0.4 kg) × (-10 m/s) - (0.4 kg) × (12 m/s)
= -4 kg·m/s - 4.8 kg·m/s
= -8.8 kg·m/s
The total change in momentum is therefore -8.8 kg·m/s.
To find the average force exerted by the pavement on the ball, you can use the impulse-momentum principle, which states that the change in momentum is equal to the impulse applied:
Impulse = Change in momentum
Force × Time = Change in momentum
Rearranging this equation, we can solve for force:
Force = (Change in momentum) / Time
Substituting the values, we have:
Force = (-8.8 kg·m/s) / (0.01 s)
= -880 N
Since the force is negative, it means that the force exerted by the pavement is in the opposite direction of the initial motion of the ball. Therefore, the average force exerted by the pavement on the ball is 880 N.
To calculate the total change in momentum, you need to find the initial and final momenta of the rubber ball.
The initial momentum (p1) can be calculated using the formula: p1 = m * v1, where m is the mass of the ball and v1 is its initial velocity. In this case, the mass is 400 g (0.4 kg) and the initial velocity can be found using the formula: v1 = ∆d / ∆t, where ∆d is the vertical distance and ∆t is the time of contact. Here, ∆d = 12 m and ∆t = 0.01 s.
So, the initial momentum (p1) can be calculated as:
p1 = m * v1 = 0.4 kg * (12 m / 0.01 s)
Next, you need to find the final momentum (p2) of the ball. The final momentum can be calculated using the formula: p2 = m * v2, where v2 is the final velocity of the ball after rebounding. The final velocity (v2) can be found in a similar way as the initial velocity, using the same formula: v2 = ∆d / ∆t. Here, ∆d = 10 m and ∆t = 0.01 s.
So, the final momentum (p2) can be calculated as:
p2 = m * v2 = 0.4 kg * (10 m / 0.01 s)
Finally, you can find the total change in momentum (∆p) by subtracting the initial momentum from the final momentum: ∆p = p2 - p1.
To calculate the average force exerted by the pavement on the ball, you can use the formula: F = ∆p / ∆t, where ∆p is the total change in momentum and ∆t is the time of contact. In this case, ∆t = 0.01 s.
So, the average force exerted by the pavement on the ball can be calculated as: F = ∆p / ∆t = (∆p) / 0.01 s.
Now, let's plug in the values into the equations and calculate the results.