Two objects of the same mass, m = 1.00 kg, are projected towards each other. The

Question

Two objects of the same mass, m = 1.00 kg, are projected towards each other. The first object initially has velocity (20.0m/s)i^. The second object has initial velocity (-10.0m/s)i^ .After the glancing collision, the first object goes off with angle 2.00? above the positive x-direction and the second object goes off with angle 5.00? below the negative x-direction.

a. What is the speed of object 1 after the collision?
b. What is the speed of object 2 after the collision?
c. What is the change in kinetic energy in the collision?
d. Is this collision elastic or inelastic? Explain.

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Explanation / Answer

a) Momentum is conserved in both x- and y-directions. In the x-direction:

Initial momentum = final momentum

or, 1 x 20 - 1 x 10 = 1 x v1cos 2 - 1 x v2cos5

or, v1 = (10 + v2cos5) / cos2 -------------------------- ( 1 )

In the y -direction:

0 = 1 x v1sin 2 - 1 x v2sin5

or, v2 =  v1sin 2/sin5

Substituting this in equation 1, we get:

v1 = (10 + v1 x cos5 x sin 2/sin5 ) / cos2

or, v1 = (10 + 0.4  v1 ) x 1

or, v1 = 10/0.6 = 16.67 m/s

b) v2 =  v1sin 2/sin5 = 16.67 x sin 2/sin5 = 6.67 m/s

c) Change in kinetic energy= 1/2 ( u12 + u22 - v12 - v22 )

= 1/2 ( 202 + 102 - 16.672 - 6.672)

= 1/2 ( 177.622)

= 88.81 J

d) The collision is inelastic since kinetic energy is not conserved.

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