Chapter 2: Forces and motion

Definition

2.1.1 What is inertia?2.1.2 Relation between inertia and mass2.1.3 Situation involving inertia2.1.4 Ways to reduce negative effects of inertia

INERTIA The inertia of an object is the tendency of the object to

remain at rest or if moving, to continue its motion in a straight line.

Newton’s first law of motion

Newton;s first law states that, “Every object continues in its state of rest or uniform motion unless it is acted upon by an external force.”

When both pail are pushed, it is found that the empty bucket is easier to push compared to the bucket with sand.

When both buckets are oscillating and an attempt is made to stop them, the bucket filled with sand is more difficult to stop.

An object with a larger mass has a larger inertia.

Relation between inertia and mass

“The larger the mass, the larger the inertia”

SITUATIONS INVOLVING INERTIA

SITUATION EXPLANATIONWhen the cardboard is pulled away

quickly, the coin drops straight into the glass.

The inertia of the coin maintains its state at rest.

The coin falls into the glass due to gravity.

The sauce inside the bottle moves together with the bottle.

When the bottle stops suddenly, the sauce continues in its state of motion due to the effect of its inertia.

SITUATION EXPLANATIONBody moves forward when the car

stops suddenly .The passengers were in a state of

motion when the car was moving. When the car stopped suddenly, the

inertia in the passengers made them maintain their state of motion.

Thus when the car stops, the passengers moved forward.

A boy runs away from a cow in a zig zag motion.

The cow has a large inertia making it difficult to change direction.

Furniture carried by a lorry normally are tied up together by string.

When the lorry starts to move suddenly, the furniture are more difficult to fall off due to their inertia because their combined mass has increased.

Ways to Reduce Negative Effects of Inertia

Safety belt Prevent driver from thrown forward due to inertia.

Safety Airbag To prevent the driver from hitting the steering wheel or dashboard during a collision.

m1 =0.02 kg

v2= 2ms-1

m2 = 1000 kg m1 = 1000 kg

v2 = 80 ms-1 v1 = 100 ms-1

v1= 2ms-1

m2 =0.05 kg

MOMENTUMIs a product of mass and velocityMomentum, p = mass × velocity

p = mvUnit: kgms-1 // Ns (vector quantity)

So if an object is moving, then it has momentum. Momentum depends upon the variables mass and velocity. Momentum is directly proportional to mass. Momentum is directly proportional to the velocity.

Principle of conservation of momentum states that in the absence of an external force, the

total momentum of a system remains unchanged.

PRINCIPLE OF CONSERVATION OF MOMENTUM

For a collision occurring between object 1 and object 2, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

Principle of conservation of momentum have 3 condition:

i) Elastic collision

ii) Inelastic collision

iii) Explosions

ELASTIC COLLISION INELASTIC COLLISION

Both objects move independently at their respective

velocities after the collision.

The two objects combine and move together with a common

velocity after the collision.

Momentum is conserved Momentum is conserved.

ELASTIC COLLISION

Total Momentum Before = Total momentum Afterm1u1 + m2u2 = m1v1 + m2v2

INELASTIC COLLISION

Total Momentum Before = Total Momentum Afterm1u1 + m2u2 = (m1 + m2) v

EXPLOSIONS

Before explosion both object stick together and at rest

After collision, both object move at opposite direction.

EXPLOSION

Total Momentum Before collision= Total Momentum After collision0 = m1v1 + m2v2

m1v1 = - m2v2

negative sign means opposite direction

When a rifle is fired, the bullet of mass m, moves with a high velocity, v. This creates a momentum in the forward direction.From the principle of conservation of momentum, an equal but opposite momentum is produced to recoil the riffle backward.

A high-speed hot gases are ejected from the back with high momentum.This produces an equal and opposite momentum to propel the jet plane forward.

EXERCISE 1

Car A of mass 1000 kg moving at 20 ms-1 collides with a car B of mass 1200 kg moving at 10 ms-1 in same direction. If the car B is shunted forwards at 15 ms-1 by the impact, what is the velocity, v, of the car A immediately after the crash? [ans:14 ms-1]

EXERCISE 2

mA = 4 kg mB = 2 kg

uA = 10 m/s to the left

uB = 8 m/s to the right

vB = 4 m/s to the left.Calculate the value of vA . [ans: 8m/s]

AB AB

EXERCISE 3

A truck of mass 1200 kg moving at 30 m/s collides with a car of mass 1000 kg which is travelling in the opposite direction at 20 m/s. After the collision, the two vehicles move together. What is the velocity of both vehicles immediately after collision? [7.27 m/s]

EXERCISE 4

A man fires a pistol which has a mass of 1.5 kg. If the mass of the bullet is 10 g and it reaches a velocity of 300 m/s after shooting, what is the recoil velocity of the pistol? [ans: -2m/s]