Prob 3 Two flat objects are sliding across the frictionless surface of a frozen

Question

Prob 3 Two flat objects are sliding across the frictionless surface of a frozen lake and approach one another as shown in the figure. They move in such a way as to collide at the origin of the coordinate system shown. After the collision object A moves off along the direction and object B moves off along the - direction. The objects have masses mA = 1.0 kg and mB = 0.25 kg and initial kinetic energies KA 1.0 J and KB 10 J. (a) What are the initial velocities (magnitude and direction, or i and j components) of the two objects? collision point 50.0 A,i A.J (b) What is the initial momentum (magnitude and direction, or i and j components) of the system of the two objects? Phot (c) Find the speeds of the two objects after the collision

Explanation / Answer

a) We are given initial kinetic energies for both objects.

KA = 1/2mAvA2

vA = sqrt (2 / 1)

vA = 1.4142 m/s

However, Object A was initially moving at an angle,

so, vA,i = 0.909 ( x - direction)

vA,i = 1.0833 ( y- direction)

vA,i = - 0.909 i - 1.0833 j

vB,i = sqrt ( 20 / 0.25)

vB,i = - 8.9443 i + 0 j

b) Momentum of object A =  - 0.909 i - 1.0833 j

Momentum of object B = - 2.2361 i + 0 j

Total momentum =  - 0.909 i - 1.0833 j + (- 2.2361 i + 0 j )

Total momentum = - 3.1451 i - 1.0833 j

c) mAvA-i + mBvB-i = mAvA-f + mBvB-f

K.EA + K.EB = 1/2 mAvA-f2 + 1/2 mBvB-f2

we have two equation two unknowns,

I will use magnitude of all values.

1.4141 - 2.236 =  mAvA-f + mBvB-f

11 =  1/2 mAvA-f2 + 1/2 mBvB-f2

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