Chapter : 2. Force & Laws Of Motion
Examples of impulse
Example : 3
A force acts for 0.2 s on a body of mass 2.5 kg initially at rest. The force then ceases to act and the body moves through 4m in the next one second. Calculate the magnitude of force.
Solution. When the force ceases to act, the body will move with a constant velocity. Since it moves a distance of 4 m in 1 s, therefore, its uniform velocity = 4m/s.
Now, initial velocity, u = 0
Final velocity, v = 4 m/s
Time interval Δt = 0.2 s
Acceleration,
20m/s2
Force, F = 2.5 × 20 = 50 N
Example : 4
A ball of mass 20 gm is initially moving with a velocity of 100 m/s. On applying a constant force on the ball for 0.5s, it acquires a velocity of 150 m/s. Calculate the following :
(i) Initial momentum of the ball
(ii) Final momentum of the ball
(iii) Rate of change of momentum
(iv) Acceleration of the ball
(v) Magnitude of the force applied
Solution. Given, m = 20 gm = 20/1000 kg = 0.02 kg
Initial Velocity, u = 100 m/s
Time interval,t = 0.5 s
Final velocity,v = 150 m/s
(i) Initial momentum of the ball = mass × Initial velocity
or P1 = mu = 0.02 kg × 100 m/s
= 2 kg-ms–1
(ii) Final momentum of the ball
= mass × final velocity
or P2 = mv = 0.02 kg × 150 m/s
= 3 kg-ms–1
(iii) Rate of change of momentum =
or
= 2.0 kg-ms–1 =2.0N
(iv) Acceleration a,
= 100ms–2
(v) Force, F = mass × acceleration = 0.02 × 100 = 2.0 N
A force acts for 0.2 s on a body of mass 2.5 kg initially at rest. The force then ceases to act and the body moves through 4m in the next one second. Calculate the magnitude of force.
Solution. When the force ceases to act, the body will move with a constant velocity. Since it moves a distance of 4 m in 1 s, therefore, its uniform velocity = 4m/s.
Now, initial velocity, u = 0
Final velocity, v = 4 m/s
Time interval Δt = 0.2 s
Acceleration,
20m/s2Force, F = 2.5 × 20 = 50 N
Example : 4
A ball of mass 20 gm is initially moving with a velocity of 100 m/s. On applying a constant force on the ball for 0.5s, it acquires a velocity of 150 m/s. Calculate the following :
(i) Initial momentum of the ball
(ii) Final momentum of the ball
(iii) Rate of change of momentum
(iv) Acceleration of the ball
(v) Magnitude of the force applied
Solution. Given, m = 20 gm = 20/1000 kg = 0.02 kg
Initial Velocity, u = 100 m/s
Time interval,t = 0.5 s
Final velocity,v = 150 m/s
(i) Initial momentum of the ball = mass × Initial velocity
or P1 = mu = 0.02 kg × 100 m/s
= 2 kg-ms–1
(ii) Final momentum of the ball
= mass × final velocity
or P2 = mv = 0.02 kg × 150 m/s
= 3 kg-ms–1
(iii) Rate of change of momentum =
or
= 2.0 kg-ms–1 =2.0N(iv) Acceleration a,
= 100ms–2(v) Force, F = mass × acceleration = 0.02 × 100 = 2.0 N
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