C:\fakepath\momentum

UNIT 4TOPIC 1: FURTHER

MECHANICS

Part 1: MOMENTUM

Prepared by: Pn Siti Fatimah Saipuddin INTEC

1

OBJECTIVES

Able to express equation p = mv Apply the principle of conservation of

momentum, m1u1 + m2u2 = m1v1 + m2v2

Special cases in collisions and energy, explosions

Apply the concept of impulse, Ft = mv-mu and force

2

LINEAR MOMENTUM

The (linear) momentum of a body is defined by: Momentum = Mass x Velocity

Exercise 2.1:A body A of mass 5 kg moves to the right with a velocity of 4 ms-1. A body of mass 3 kg moves to the left with a velocity of 8 ms-1. Calculate:

The momentum of A [ +20 kg ms-1] The momentum of B [ -24 kg ms-1] The total momentum of A and B [ -4 kg ms-1]

3

CONSERVATION OF MOMENTUM

Provided that no external forces are acting, it can be assumed that when collision happens between two bodies, the total momentum before collision is the same as that after collision.

This means that: m1u1 + m2u2 = m1v1 + m2v2

4

CONSERVATION OF MOMENTUM

Exercise 2.2:

A 2.0 kg object moving with a velocity of 8.0 ms-1 collides with a 4.0 kg object moving with a velocity of 5.0 ms-1 along the same line. If the two objects join together on impact, calculate their common velocity when they are initially moving

In the same direction [ 6.0 ms-1] In opposite direction [ -0.67 ms-1]

5

COLLISIONS AND ENERGY Momentum is conserved in a collision. Total energy is

also conserved but the kinetic energy might not be conserved. It can be converted to other forms such as sound, work done during plastic deformation, etc.

In an elastic collision: Kinetic energy is conserved Linear momentum is conserved Energy is conserved

In a non-elastic collision: Kinetic energy is not conserved Linear momentum is conserved Energy is conserved

In a completely inelastic collision: The objects stick together on impact 6

COLLISIONS AND ENERGY Exercise 2.3:

Calculate the KE converted to other forms during the collisions in (a) and (b) of Exercise 2.2

KE converted = [ 6J ] KE converted = [ 113J ]

  Exercise 2.4: 

A 2.0 kg object moving with velocity 6.0 ms-1 collides with a stationary object of mass 1.0 kg. Assuming that the collision is perfectly elastic, calculate the velocity of each object after the collision. [v1 = 2.0 ms-1 and v2 = 8.0 ms-1] 7

COLLISIONS AND ENERGY

Example: Two particles S of mass 30g and T of mass

40g, both travel at the speed of 35 ms-1 in directions at right angles to each other. The two particles collide and stick together. Calculate their speed after the impact.

[ 25.0 ms-1 ]

8

T

S

EXPLOSIONS An object explodes as a result of some internal

forces. As the result, the total momentum of the separate parts will be the same as that of the original body, which is normally zero.

Exercise 2.4: 

Figure below shows two trolleys A and B initially at rest, separated by a compressed spring. The spring is now released and the 3.0 kg trolley moves with a velocity of 1.0 ms-1 to the right. Calculate:

The velocity of the 2.0 kg trolley [-1.5 ms-1] The total KE of the trolleys [3.75J]

9

IMPULSE AND FORCE If a force, F acts on a body of mass, m for a time, t

so that the velocity of the body changes from u to v, then:

F = (rate of change of momentum) = (mv-mu)

tFt = mv – mu = impulse

Exercise 2.5:A stationary golf ball is hit with a club which exerts an average force of 80 N over a time of 0.025 s. Calculate:

The change in the momentum [2.00 kg ms-1] The velocity acquired by the ball if it has a mass of

0.020 kg [ 100 ms-1]

10

IMPULSE AND FORCE

Exercise 2.6:

Figure below shows how the force acting on a body varies with time. The increase in momentum of the body, measured in Ns as the result of this force acting for four seconds is _________

[24 Ns]11

FRICTION Friction is the force that opposes the relative motion

between two solid surfaces which are in contact. The frictional force before relative motion between the

surfaces occurs is known as static friction. Limiting static friction, Fs = μsR

The limiting static friction, Fs between two surfaces just before relative motion occurs.

Independent of the surface area of contact

Kinetic friction, Fk = μkR The friction between two surfaces when there is

relative motion between the surfaces Independent of the surface area of contact and the

relative speed between the surfaces

The value of coefficient: μk < μs

12

SUMMARY Momentum, p = Mass, m x Velocity, v Principle of conservation of momentum states that: m1u1 + m2u2 = m1v1 + m2v2

In an elastic collision: Kinetic energy, Linear momentum, and Energy

are conserved In a non-elastic collision:

Kinetic energy is not conserved Linear momentum and Energy are conserved

Ft = mv – mu = impulse Limiting static friction, Fs = μsR Kinetic friction, Fk = μkR μk < μs

13

ONE-DIMENSIONAL COLLISION

14

ELASTIC COLLISION PERFECTLY INELASTIC COLISION

TWO-DIMENSIONAL COLLISION

15

EXAMPLE:

A 1500kg car traveling east with the speed of 25 ms-1 collides at an intersection with a 2500kg van traveling north at a speed of 20ms-1. find the direction and the magnitude of the velocity of the wreckage after the collision, assuming that the collision undergoes perfectly inelastic collision

16θ = 53.1°vf = 15.6 ms-1