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In this lesson, we will learn how to use Newton's law of restitution to solve problems about the impact of two smooth spheres.

Q1:

A body π΄ of mass 5 kg, moving with a velocity β π£ = 2 β π + β π / 1 m s , collided with another body π΅ , of mass 10 kg that was moving with a velocity β π£ = β 6 β π β 3 β π / 2 m s . After the impact, if the velocity of body π΄ became β π£ = β 6 β π β 3 β π / β² 1 m s , determine the speed of body π΅ .

Q2:

Two spheres, π΄ and π΅ , have equal radii and are moving across a smooth horizontal surface. Sphere π΄ has a mass of 4 kg and is moving with velocity ( 3 ) j m/s. Sphere π΅ has a mass of 5 kg and moves with a velocity ( β 3 ) i j m/s. The spheres collide when the line of their centres is parallel to j . Sphere π΄ has a velocity of π£ 1 immediately after the impact and sphere π΅ has a velocity of π£ 2 immediately after the impact. Find the velocities π£ 1 and π£ 2 in vector form, taking the coefficient of restitution between the spheres to be 1 2 .

Q3:

Two smooth spheres of equal radii and masses π kg and 5 π kg collided while moving on a smooth horizontal surface. Before the collision, the sphere of mass π kg was moving at ( 9 + 5 ) i j m/s and the sphere of mass 5 π kg was moving at ( β 5 ) i j m/s. After the collision, the sphere of mass π kg was moving at ( 5 + 7 ) i j m/s. Find the speed of the sphere of mass 5 π kg after the collision.

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