The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 5 s. Find (a) the momentum before the action of force (b) the momentum after the action of force (c) the magnitude of force.
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The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 5 s. Find (a) the momentum before the action of force (b) the momentum after the action of force (c) the magnitude of force.
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Answer
Initial momentum = 40 kg.m/s
Final momentum = 80 kg.m/s
Magnitude of force = 8 N
Given
Mass of a body , m = 10 kg
Initial velocity , u = 4 m/s
Final velocity , v = 8 m/s
Time , t = 5 s
To Find
a . Momentum before the action of force
b . Momentum after the action of force
c . Magnitude of force
Formula Applied
Momentum is defined as product of mass and velocity'
where ,
Force is defined as product of mass and acceleration
where ,
Solution
a . Momentum before the action of force
velocity before action of force is ,
Initial velocity , u = 4 m/s
mass , m = 10 kg
Initial Momentum , P = ? kg.m/s
So ,
⇒ P = mu
⇒ P = (10)(4)
⇒ P = 40 kg.m/s
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b . Momentum after the action of force
Velocity after action of force is ,
Final velocity , v = 8 m/s
Mass , m = 10 kg
Final Momentum , P = ? kg.m/s
So ,
⇒ P = mv
⇒ P = (10)(8)
⇒ P = 80 kg.m/s
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c . The magnitude of force
Acceleration is defined as rate of change in velocity .
Now ,
So , Magnitude of the force = 8 N
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