# Worksheet: Oblique Impact

In this worksheet, we will practice solving problems about oblique impact of objects in two dimensions involving using conservation of momentum and coefficient of restitution.

Q1:

A body of mass 5 kg, moving with a velocity , collided with another body , of mass 10 kg that was moving with a velocity . After the impact, if the velocity of body became , determine the speed of body .

• A m/s
• B m/s
• C m/s
• D m/s

Q2:

Two spheres, and , have equal radii and are moving across a smooth horizontal surface. Sphere has a mass of 3 kg and is moving with velocity m/s. Sphere has a mass of 6 kg and moves with a velocity m/s. The spheres collide when the line of their centres is parallel to . Sphere has a velocity of immediately after the impact and sphere has a velocity of immediately after the impact. Find the velocities and in vector form, taking the coefficient of restitution between the spheres to be .

• A ,
• B ,
• C ,
• D ,
• E ,

Q3:

Two smooth spheres of equal radii and masses kg and kg collided while moving on a smooth horizontal surface. Before the collision, the sphere of mass kg was moving at m/s and the sphere of mass kg was moving at m/s. After the collision, the sphere of mass kg was moving at m/s. Find the speed of the sphere of mass kg after the collision.

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q4:

A smooth sphere of mass kg was sliding on a smooth horizontal plane when it collided with another, initially stationary, smooth sphere of the same size and a mass of kg. The first sphereβs direction of motion after the collision was at right angles to its direction of motion before the collision. Let be the angle the first sphereβs direction of motion made with the line of centres of the spheres just before impact. Find an expression for in terms of the coefficient of restitution between the two spheres, .

• A
• B
• C
• D
• E

Q5:

A small smooth sphere of mass 6 kg was moving in the -plane with a velocity of m/s. The sphere collided with a smooth vertical wall coincident with the line . Assuming the coefficient of restitution between the sphere and the wall is , find the amount of kinetic energy lost due to the collision. Give your answer correct to the nearest two decimal places.

Q6:

Sphere was moving at a velocity of m/s on a smooth horizontal plane when it collided with sphere . After the collision its velocity became m/s. Find a unit vector parallel to the line of centres of the spheres at the instant of collision.

• A
• B
• C
• D
• E

Q7:

A small smooth sphere moving in the -plane collided with a smooth vertical wall, where the -axis is, with a velocity of m/s. The coefficient of restitution between the sphere and the wall is . What is the sphereβs speed after impact? Give your answer correct to two decimal places.

Q8:

A smooth ball of mass 730 g fell vertically and struck a smooth plane inclined at an angle of to the horizontal. The ballβs speed just before it hit the plane was 8 m/s and the coefficient of restitution between the ball and the plane is . Determine the magnitude of the impulse received by the ball at the moment of impact. Give your answer in newton seconds correct to two decimal places.

Q9:

Two smooth spheres of the same radius are moving on a smooth horizontal surface. One sphere has a mass of 2 kg and moves with velocity m/s. The other sphere has a mass of 4 kg and moves with velocity m/s. At the moment the spheres collide, the line between their centres is parallel to . If the coefficient of restitution between the spheres is , find the kinetic energy lost in the impact.

Q10:

A small smooth ball of mass 6 kg was moving with velocity m/s when it hit a smooth wall. It rebounded from the wall with velocity m/s. Find the magnitude of the impulse received by the ball.

Q11:

A small smooth ball of mass 5 kg was moving with velocity m/s when it hit a smooth wall. It rebounded from the wall with velocity m/s. Find the magnitude of the impulse received by the ball.

Q12:

A smooth sphere moving on a smooth horizontal surface at a velocity of m/s collided with another smooth sphere of the same radius but half the mass, which was moving at m/s. Given that, after the collision, the first sphereβs velocity became m/s, find the coefficient of restitution between the spheres.

• A
• B
• C
• D
• E