This set of Advanced Machine Kinematics Questions and Answers focuses on “Loss of Kinetic Energy During Elastic Impact”.

1. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the loss of kinetic energy when the collision is inelastic.

a) 18.75 N-m

b) 19.75 N-m

c) 17.75 N-m

d) 16.75 N-m

View Answer

Explanation: Loss of kinetic energy during inelastic collision is given by

m

_{1}m

_{2}/(2(m

_{1}+ m

_{2}) (u

_{1}

^{2}– u

_{2}

^{2})

substituting the values we get

El = 18.75 N-m.

2. The coefficient of restitution is 0 for a completely inelastic collision.

a) True

b) False

View Answer

Explanation: For a completely inelastic collision the bodies stick to each other after collision, hence there is no relative velocity after collision therefore the coefficient of restitution is 0.

3. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the loss of kinetic energy when the collision is inelastic with e = 0.6.

a) 18.75 N-m

b) 12.00 N-m

c) 13.75 N-m

d) 12.75 N-m

View Answer

Explanation: Loss of kinetic energy during inelastic collision with coefficient of restitution is given by

m

_{1}m

_{2}/(2(m

_{1}+ m

_{2}) (u

_{1}

^{2}– u

_{2}

^{2})(1-e

^{2}))

substituting the values we get

El = 12 N-m.

4. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the common velocity in m/s after collision when the collision is completely inelastic.

a) 2.5

b) 9.75

c) 7.25

d) 6.75

View Answer

Explanation: Common velocity during inelastic collision is given by

m

_{1}u

_{1}+ m

_{2}u

_{2}/(m

_{1}+ m

_{2}) = v

substituting the values we get

V = 2.5 m/s

5. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 50 Kg mass in m/s after collision when the collision is elastic.

a) 2.5

b) 2.00

c) 7.25

d) 6.75

View Answer

Explanation: Velocity during elastic collision is given by

m

_{1}u

_{1}+ m

_{2}u

_{2}/(m

_{1}+ m

_{2}) = v

substituting the values we get

V = 2.5 m/s

v

_{1}= 2V – u

_{1}

v

_{1}= 2m/s

6. Coefficient of restitution of elastic bodies is ______

a) One

b) More than one

c) Between 0 and one

d) Zero

View Answer

Explanation: In case of elastic bodies the relative velocity after collision is equal to the relative velocity before collision, hence the coefficient of restitution is 1.

7. Kinetic energy before collision is always equal to the kinetic energy after collision.

a) True

b) False

View Answer

Explanation: Kinetic energy before collision is equal to the kinetic energy after collision only in case of elastic collisions, in other cases energy is lost during deformation.

8. Which of the following cases has the greatest loss in Kinetic energy?

a) e=0

b) e=1/2

c) e=1/4

d) e=1

View Answer

Explanation: e=0 signifies that the collision was completely inelastic, in case of completely inelastic collisions the Kinetic energy loss after collision is maximum.

9. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 25 Kg mass in m/s after collision when the collision is elastic.

a) 2.5

b) 2.00

c) 3.5

d) 6.75

View Answer

Explanation: Velocity during elastic collision is given by

m

_{1}u

_{1}+ m

_{2}u

_{2}/(m

_{1}+ m

_{2}) = v

substituting the values we get

V = 2.5 m/s

v

_{2}= 2V – u

_{2}

v

_{2}= 3.5 m/s

10. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 25 Kg mass in m/s after collision when the collision is inelastic with e = 0.6.

a) 2.5

b) 2.00

c) 3.5

d) 3.1

View Answer

Explanation: Velocity during elastic collision is given by

m

_{1}u

_{1}+ m

_{2}u

_{2}/(m

_{1}+ m

_{2}) = v

substituting the values we get

V = 2.5 m/s

v

_{2}= 2(1+e)V – eu

_{2}

v

_{2}= 3.1 m/s.

11. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 50 Kg mass in m/s after collision when the collision is inelastic with e = 0.6.

a) 2.2

b) 2.00

c) 3.5

d) 3.1

View Answer

Explanation: Velocity during elastic collision is given by

m

_{1}u

_{1}+ m

_{2}u

_{2}/(m

_{1}+ m

_{2}) = v

substituting the values we get

V = 2.5 m/s

v

_{1}= 2(1+e)V – eu

_{1}

v

_{1}= 2.2 m/s.

12. Which of the following cases momentum is conserved?

a) Perfectly elastic collision

b) Inelastic collision with 0<e<1

c) Perfectly inelastic collision

d) Momentum is always conserved

View Answer

Explanation: When the net external force acting on the body is 0, the linear momentum is always conserved no matter the type of collision.

13. Which of the following cases Kinetic energy is conserved?

a) Perfectly elastic collision

b) Inelastic collision with 0<e<1

c) Perfectly inelastic collision

d) Momentum is always conserved

View Answer

Explanation: When the net external force acting on the body is 0, the linear momentum is always conserved no matter the type of collision, however in only completely elastic collisions the kinetic energy of the system remains conserved.

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