Newton’s second Law of Motion

Question 1 State Newton’s second law of motion?

Question 2 State the relationship between momentum and acceleration?

Question 3 If the mass of a body and the force acting on it are both doubled,what happens to the acceleration?

Question 4 Explain why a cricket player moves his hand backwards while catching a fast cricket ball?

Question 5 Find the acceleration produced by a force of 5 N acting on a mass of 10 kg?

Question 6 What is the force which produces an acceleration of 1  m/ s²  

Question 7 Why does a  high jumping athlete is provided either a cushion or a heap of sand on the ground to fall upon?

Newton’s Second law of Motion

case 1:Cricket ball(more mass)
Tennis ball(less mass)
If we throw both with same speed,it will be found that more force is required to stop cricket ball than tennis ball.The force required to stop a moving body is directly proportional to its mass.
Case 2:Two cricket balls(same mass)
Throw them with different speed
More force is required to stop that cricket ball which is moving with higher velocity than other one(moving with slow velocity)
The force required to stop a moving body is directly proportional to velocity or speed.
The quantity of motion in a body depends on the mass and velocity of the body.
The momentum of a body is defined as product of its mass and velocity.
p=m*v
If a body is at rest,its velocity is zero and hence its momentum is also zero.

Momentum is a vector quantity.

S.I. unit of momentum is kg m/s.

Momentum depend on mass and velocity of a body .

Large momentum is due to large mass or large velocity or both is large.

1)A karate player can break a pile of tiles or a slab of ice with a single blow of his hand because they strike them very very fast.In doing so,the large momentum of fast moving hand is reduced to zero in a very short time.This exerts a large force on piles of tiles.

2)A cricket ball is not very heavy but when it is thrown with high velocity,it acquires a large momentum and sometimes hurts the batsman.

3)A car or bus may not be running at high speed but because of its high mass,it has a very high momentum which may hurt the person coming on its way.

4)The road accidents at high speed are very much worse than accidents at low speed because momentum of vehicle is very high.

Momentum is measure of quantity of motion of a body.

The rate of change of momentum of a body is directly proportional to applied force and takes place in the direction in which force acts.

Force is directly proportional to change in momentum and inversely proportional to time taken.

Consider a body with mass m,Initial momentum(mu) and Final momentum (mv)
Force is directly proportional to (mv-mu) and inversely proportional to time.
Force is proportional to mass and acceleration.
k is a constant
If K=1
then
F=m*a
When a force acts on a body,it produces acceleration.
     F
a=—
    m
Acceleration produced by a body is directly proportional to force acting on it and inversely proportional to mass of body.

If the mass of a body is doubled,acceleration will be halved.

If the mass of a body is halved,acceleration will be doubled.

It will be easier to move light bodies(less mass) than heavy bodies(large mass)

S.I. unit of force is newton.

A newton is that force which when acting on a body of  mass 1 kg produces an acceleration of 1 m/ s^{2 .}

First law of motion is a special case of second law of motion because when applied force is zero,then acceleration is also zero and body remains in state of rest or uniform motion.

If a minus sign comes with the force,it will indicate that force is acting in a direction opposite to that in which body is moving.

Application of Newton’s Second law of Motion
1)Catching a Cricket Ball : A cricket player moves his hands backwards on catching a fast moving cricket ball.
Reason:A fast moving ball has large momentum.In catching this ball,its momentum has to be zero.When a cricket player move back his hands,the time taken to reduce the momentum of ball to zero is increased.Due to more time taken to stop the ball,rate of change of momentum of ball is decreased and hence small force is exerted on the hands of players.So player do not get hurt.

If cricket player stops a fast moving ball suddenly,then large momentum of ball will be reduced to zero in a very short time.Due to this,rate of change of momentum of cricket ball will be very large and hence it will exert a large force on player’s hand.

2)A high jumping athlete is provided either a cushion or a heap of sand on the ground to fall upon: This is done to prevent injury to athlete.When the high jumper falls on a soft landing site,then jumper takes a longer time to come to a stop.The rate of change of momentum of athlete is less due to which smaller stopping force acts on the athlete.Thus cushion or sand being soft,reduces the athlete’s momentum more gently.

But if athlete falls on hard ground,then momentum will be reduced to zero in a very short time.The rate of change of momentum will be large due to which large opposing force will act and cause injuries.

3)Use of seat belt in cars:In a car accident,a fast running car stop suddenly.Due to this car’s large momentum is reduced to zero in a very short time.The stretchable seat belts increases the time taken by passengers to fall forward.Due to longer time,the rate of change of momentum of passengers is reduced and hence less stopping force acts on them.Hence seat belts reduces the passenger’s momentum more gently and prevent injuries.