A smooth horizontal track carries two small spheres

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A smooth horizontal track carries two small spheres. Sphere

P

of mass

0.50\,\text{kg}

moves to the right with speed

4.0\,\text{m s}^{-1}

and strikes stationary sphere

Q

of mass

0.30\,\text{kg}

. The coefficient of restitution for their mutual collision is

e_1=0.80

. Immediately after this, sphere

Q

travels a distance of

1.2\,\text{m}

and strikes a rigid vertical wall which is fixed to the track. The coefficient of restitution for the collision with the wall is

e_2=0.60

. Neglect all friction. (i) Calculate the speeds of spheres

P

and

Q

immediately after their mutual collision. (ii) Determine the speed of sphere

Q

just after it rebounds from the wall. (iii) The two spheres now move towards one another and collide again. Find the speed of sphere

P

immediately after this second collision. (iv) Compute the percentage loss of kinetic energy of the system between the instant just before the first collision and the instant just after the second collision.

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