Question

an object of mass 100kg is accelerated uniformly from velocity of 5m/s to 8m/s in 6 second.calculate initial and final momentum of the object.also find the magnitude of force exerted on the object?​

Answer 1

Given:

• Mass of a object is 100kg.
• Initial velocity is 5m/s.
• Final velocity is 8m/s.
• Time taken to increase velocity is 6s.

To Find:

• The initial and final momentum of the object.
• The magnitude of force exerted.

Answer:

Given mass = 100kg.

Initial velocity = 5m/s.

Final velocity = 8m/s .

Now , we know that

☞ Momentum = mass × velocity

Let initial momentum be $\sf{p_1}$ and final momentum be $\sf{p_2}$

=> $\sf{ p_1 = m \times (initial\: velocity)}$

=> $\sf{p_1 = 100kg\times 5ms^{-1}}$

=> $\bf{\red{ p_{1} = 500N-m/s}}$

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=> $\sf{ p_2= m \times (final\: velocity)}$

=> $\sf{p_2= 100kg\times 8ms^{-1}}$

=> $\bf{\red{ p_{2} = 800N-m/s}}$

Now by " Newton's second law of motion"

• Rate of change of momentum is directly proportional to the applied force in the direction of the force.

=> Force (F) = ∆p/t

=> F = (800-500)N-m/s / 6s.

=> F = 300 N-m/s / 6

=> $\bf{\red{ Force = 50N}}$

Hence the applied force is 50N.