Rate of Change in Momentum of a body is directly proportional to applied UNBALANCED force
Also it takes place in direction of Force
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Newton's Second Law of Motion is basically
Force = Mass x Accelration
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We know that
Momentum = Mass x Velocity
Change in Momentum = Mass x Change in Velocity
Change in Momentum = Mass x (New Velocity - Old Velocity) Β = m x (v - u)
Why a fielder pulls his hands backwards while fielding the ball
He does it to increase the amount of time while catching a ball .This reduces the rate of CHANGE of momentum and applied force
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When a fielder catches a moving ball, it actually brings velocity of ball to 0 in very short span of time
This means that there is very high change in momentum when the fielder catches a ball
Explanation
As per Newton's second law of Motion
Force = Change in Momentum/Time = m (v - u)/t
(Hence force is inversely propirtional to time, More the time less the force and less the time more the force)
If fielder catches ball suddenly, it will take less time and hence there will be more force of ball on players hand which may hurt the fielder
If he moves back, he increases the time due to less force on players hand and he is not hurt
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Example
Suppose weight of ball was 600 grams = 0.6 kg
Suppose ball was moving at speed of 10 meters/second
When fielder catches ball, ball stops moving and velocity becomes 0
Weight of ball = 600 grams = 0.6 kg
Increase in Momentum = 10 - 0 = 10
Change in Momentum = Mass * (New Velocity - Old Velocity)
= 0.6 x (10 - 0)
= 6 kg m/s
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Suppose fielder catches this ball in 2 seconds,
Force = Change in Momentum/Time = 6/2 = 3
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Suppose fielder moves back and catches this ball in 3 seconds,
Force = Change in Momentum/Time = 6/3 = 2
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Hence applied force decreases if fielder moves backwards
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Why a high jumper is provided cushion or heap of sand on falling
A cushion or a heap of sand is provided to prevent injury to the athlete when he falls down after making a high jump.
When the athlete falls on a cushion or a heap of sand, then the jumper takes a longer time to come to rest.
The rate of change of momentum of the athlete is less due to which a smaller stopping force acts on the athlete. And hence, the athlete doesnt get hurt.
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How seat belts prevent injury in cars
In a car accident, a fast running car stops suddenly.
Due to this, the large momentum of the car reduces to zero in a very short time.
The seat belts worn by the passengers increase the time taken by the passengers to fall forward.
Due to longer time, the rate of change of momentum is reduced.
This results in less or no injury.
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How a karate player breaks slab of bricks in single blow
It is due to very high amount of momentum produced in a very short span of time
Explanation
When hands of karate player move, they carry velocity
When the hands touch the ice,the velocity is brought down to 0
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The hands of karate player moves very fast
Hence a large amount of change in momentum obtained in very short span of time
As per Newton's second law of Motion
Force = Change in Momentum/Time
(Hence force is inversely propirtional to time, More the time less the force and less the time more the force)
Since in this case, karate player takes very less time, there Is very high rate of change in momentum and hence high unbalanced force
This high unbalanced force breaks the bricks
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Questions
Example 9.1 - A constant force acts on an object of mass 5 kg for a duration of 2 s. It increases the objectβs velocity from 3 m s ^{ β1 } to 7 m s ^{ β1 } . Find the magnitude of the applied force. Now, if the force was applied for a duration of 5 s, what would be the final velocity of the object?
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Example 9.3 - A motorcar is moving with a velocity of 108 km/h and it takes 4 s to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcar if its mass along with the passengers is 1000 kg.
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NCERT Question 16 - An object of mass 100 kg is accelerated uniformly from a velocity of 5 m sβ1 to 8 m sβ1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.