1) a) A 83.0 kg fullback is running at 3.86 m/s to the east and is stopped in 0.

Question

1) a) A 83.0 kg fullback is running at 3.86 m/s to the east and is stopped in 0.760 s by a head-on tackle by a tackler running due west.

Calculate the original momentum of the fullback.

2) A 0.420 kg ice puck, moving east with a speed of 3.12 m/s, has a head-on collision with a 0.890 kg puck initially at rest. Assuming a perfectly elastic collision, what is the speed of the lighter puck? Use east as the positive axis.

What is the speed of the heavier puck?

3) A ball with a mass of 0.65 kg is dropped on a table.

The initial height of the ball is 0.85 meters.
After the ball hits the table it rebounds to a height of 0.67 meters.
The time that the ball is in contact with the table is 0.017 seconds.
Note that this is not a purely elastic or inelastic collision.

Calculate the change in the momentum of the ball during its collision with the table.

Calculate the change in kinetic energy of the ball during its collision with the table.

Thank you

Explanation / Answer

1) a) momentum = 83 * 3.86 = 320.38 i^


b) final momentum = 0

so impulse = final - initial = - 320.38 i^


c)
impulse on tackler = 320.38 i^

d) force = momentum / time = 320.38 / 0.76 = 421.552632 N i^


2)
speed of the lighter puck is given by

v1 = [ u1*(m1 - m2 ) + 2 m2 *u2 ] / [ m1 + m2 ]
m1 = 0.42
m2 = 0.89
u1 = 3.12
u2 = 0

so speed of ligher puck = v1 = -1.1193893 m/sec

speed of heavier = (m1u1 - m1v1 )/m2 = 0.42 * ( 3.12 + 1.1193893 ) / 0.89 = 2.000611 m/sec

3)
speed of the ball just before coliding with table = sqrt ( 2 * g * h ) = sqrt ( 2*9.8 *0.85 ) = 4.08167 m/sec

final speed of the ball after collison = sqrt ( 2 * 9.8 * 0.67) = 3.62381015 m/sev upewards


intial momentum = 0.65 * 4.08167 = 2.6530855 (-j^)

final momentum = 0.65 * 3.62381015 = 2.3554765975 j^

so change in momentum = final - initial = 2.3554765975j^ - 2.6530855 (-j^)
= 5.0085620975 j^

b) average force = change in monetum / time = 5.0085620975 / 0.017 = 294.6213 N j^

intial kinetic energy = 0.5 * 0.65 * 4.08167^2 = 5.4145097463925 J
final kinetic energy = 0.5 * 0.65 * 3.62381015^2 = 4.2679 J

so change in k..e = final - intial = 4.2679 - 5.4145097463925 = - 1.1466097463925 J

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