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Physics Help >> Index to Physics Homework Help » Planar Momentum


 

EXAMPLE MOMENTUM PROBLEMS

 

1. Two ice skaters, Daniel (mass 65.0 kg) and Rebecca (mass 45.0 kg), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00 m/s at an angle of 53.1 degrees from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

a) What is the magnitude of Daniel's velocity after the collision?
b) What is the direction of Daniel's velocity after the collision? (degrees from the Rebecca's original)
c) What is the change in total kinetic energy of the two skaters as a result of the collision?

2. A skater with a mass of 80.0 kg is traveling due east at 4.00 m/s when she collides with another skater of mass 55.0 kg heading due south at 16.0 m/s. If they stay tangled together, what is their final velocity?

3. A woman and her husband simultaneously dive from a 120 kg raft that is initially at rest. The woman (60 kg) jumps from the boat with a horizontal speed of 1.9 m/s due south, while her husband (77 kg) jumps with a horizontal speed of 1.5 m/s due west. Calculate the magnitude and direction of the boat’s velocity immediately after their dives.

 

ANSWERS TO EXAMPLE MOMENTUM PROBLEMS

1. Momentum before the collision and the momenta of the two skaters, parting at right angles, after the collision are ilustrated in this diagram.

 

 

 

 

 

 

 

This diagram illustrates the total momentum before the collision and the momenta of the two skaters after the collision.

 

 

 

 

 

Total momentum is conserved. This diagram illustrates the sum of the momentum vectors after skaters collide is the total momentum of the skaters before the collision.

 

 

This diagram illustrates conservation of momentum, showing the total momentum before the collision equal to the sum of the momenta of the skaters after the collision.

 

 

 

 

The momentum of each skater is related to the initial momentum by the sine of the opposite angle. Once you have the momentum of a skater, you can find velocity because you were given the mass.

 

Knowing the mass and momentum of each skater, you can now calculate the kinetic energy of each, and finally the change in kinetic energy from Rebecca's original kinetic energy.

 

2.

Total momentum is a vector sum.

The initial momenta and total momentum are illustrated to the left.

 

p1 = (80)(4.00)

 

p2 = (55.0)(16.0)

 

pTOT = √(p12 + p22 )

 

ø = tan-1( p1 / p2)

 

After the collision pTOT is the same as above.

 

Since pTOT = (80 +55)v , solve for v, the only unknown.

 

3. Immediately after diving the momenta of the woman is 114 kg-m/s [S] and of the man is 115.5 kg-m/s [W].

To cancel the two components, the resultant must be an equilibrant.

 

Since the total momentum before the event was zero, the momenta of the man, woman and boat after the event must add to zero.

 

ø = tan-1( 114/115.5) = 44.6º

 

The momentum of the boat after the event is given by

 

√(1142 + 115.52) = 162 kg-m/s

 

Since v = p/m, v = (162 kg-m/s) / (120 kg) = 1.35 m/s

 

The velocity of the raft is 1.35 m/s 135.4º away from the velocity of the man.

 

 

A. COLLISIONS WITHOUT COUPLING

1. A pendulum consists of a 0.8 kg bob attached to a string of length 2.3 m. A block of mass m rests on a horizontal frictionless surface. The pendulum is released from rest at an angle of 53° with the vertical and the bob collides elastically with the block at the bottom of the swing. Following the collision, the maximum angle of the pendulum with the vertical is 5.73°. Determine the two possible values of the mass m.

 

B. COLLISIONS WITH COUPLING

1. Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 14.5 m/s

 

toward the east and the other is traveling north with speed v2. The vehicles collide in the intersection and

 

stick together, leaving parallel skid marks at an angle of 52.0° north of east. What was the initial speed of the

 

northward-moving vehicle?

 

2. A 12 g bullet traveling at 500 m/s strikes an 0.8 kg block of wood that is balanced on a table edge 0.8 m above ground. If the bullet buries itself in the block, find the distance D at which the block hits the floor.

 

3. A 1.8-kg block, initially at rest, slides down a frictionless ramp that is angled at 35 degrees to the horizontal. At a point 0.45 m down the slope it collides with and sticks to a stationary block of mass 1.1 kg. The blocks then continue another 0.88 m down the ramp. How long does the whole event take?

 

C. EXPLOSIONS

1. A plane flying horizontally, releases a bomb, which explodes before hitting the ground. Neglecting air resistance, the center of mass of the bomb fragments, just after the explosion is ( zero , along parabolic path, moves horizontally, moves vertically ).

 

2. A small explosive charge is placed in a rubber block resting on a smooth surface. When the charge is detonated, the block breaks into three pieces. A 200-g piece travels at 1.4 m/s, and a 300-g piece travels 0.90 m/s. The third piece flies off at a speed of 1.8 m/s. If the angle between the first two pieces is 80 degrees, calculate the mass and direction of the third piece.

 


ANSWERS to MOMENTUM PROBLEMS

For solutions to all the problems on this page click here.