Chapter 3: Dynamics

Question 1

Define mass

Answer 1

The mass of a body is a measure of its resistance to change in state of motion.
It is a scalar qty and has SI unit kg

Question 2

Define momentum

Answer 2

The momentum of a body is defined as the product of its mass and its velocity
It is a vector qty and has SI unit kg m s^-1

Question 3

State the equation for momentum

Answer 3

p = mv

Question 4

Define force

Answer 4

The force acting on a body is defined as the rate of change of momentum of the body
It is a vector qty and its SI unit is N

Question 5

State the equation of force

Answer 5

F = dp/dt

Question 6

Define impulse

Answer 6

The impulse on the body is the product of the force acting on it and the time of impact of the force
It is a vector qty and has SI unit N s

Question 7

State the equation of impulse

Answer 7

Impulse = F t
Impulse = Area under F-t graph

Question 8

State Newton’s First Law of Motion

Answer 8

Newton’s First Law of Motion states that a body will continue to be at rest or continue to move at constant velocity unless a resultant external force acts on it

Question 9

State Newton’s Second Law of Motion

Answer 9

Newton’s Second Law of Motion states that the rate of change of momentum of a body is proportional to the resultant external force acting on it and the change in momentum is in the direction of the force

Question 10

State Newton’s Third Law of Motion

Answer 10

Newton’s Third Law of Motion states that when body A exerts a force on body B, body B exerts a force equal in magnitude and opposite in direction on body A

Question 11

State the principle of conservation of linear momentum

Answer 11

The principle of conservation of linear momentum states that the total momentum of the bodies in the system remains constant if there is no resultant external forces acting on it

Question 12

What is a (perfectly) elastic collision?

Answer 12

It is a collision in which the total kinetic energy after the collision is equal to that before the collision.
i.e. all kinetic energy converted to elastic energy during the collision is converted back to kinetic energy after the collision. Thus, relative speed of approach = relative speed of separation: u1 - u2 = v2 - v1

Question 13

What is inelastic collision?

Answer 13

It is a collision in which the total kinetic energy after the collision is less than that before the collision.
i.e. not all kinetic energy that is converted into elastic energy during the collision are converted back to kinetic energy after the collision.Thus, relative speed of approach > relative speed of separation: u1 - u2 > v2 - v1

Question 14

What is a perfectly inelastic collision?

Answer 14

It is when the loss in total kinetic energy is so great such that the bodies do not separate but move together with a common velocity subsequently -> total initial K.E. = total final K.E. + max loss

Question 15

What is a superelastic collision?

Answer 15

It is when total kinetic energy after a collision is more than before, such as in an explosion. Thus, relative speed of separation > relative speed of approach. Total final K.E. = total initial K.E. + increase

Question 16

Prove that in a (perfectly) elastic collision, relative speed of approach = relative speed of separation

Answer 16

For 2 bodies to collide, u1 > u2
For 2 bodies to separate, v1 < v2
For momentum to be conserved, m1u1 + m2u2 = m1v1 + m2v2 — (1)
For kinetic energy to be fully recovered, 1/2 m1 u1^2 + 1/2 m2 u2^2 = 1/2 m1 v1^2 + 1/2 m2 v2^2 — (2)
From (1): m1(v1 - u1) = -m2(v2 - v1) — (3)
From (2): m1 (v1^2 - u1^2) = -m2(v2^2 - v1^2) — (4)
(4) / (3): v1 + u1 = v2 + u2
—> u1 - u2 = v2 - v1