Question

An object of mass 100 kg is accelerated uniformly from a velocity of 5 m/s to 8 m/s in 6s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.​

Answer 1

Given:

• Mass of an object, m = 100kg
• Initial velocity of an object, u = 5 m/s.
• Final velocity of an object, v = 8 m/s.

To Find:

• The initial and final momentum of an object.
• Magnitude of the force exerted on the object.

Formulas used:

• P = mv
• $\bf F = \dfrac{m(v-u)}{t}$

Where,

➠ P = Momentum

➠ m = Mass of an object

➠ V = Final velocity

➠ F = Force

➠ u = Initial velocity

➠ t = Time taken

Solution:

The initial momentum of the object,

• P = mu
• 100 × 5
• 500 kg m/s

The final momentum of the object,

• P = mv
• 100 × 8
• 800 kg m/s

Now,

Force = Rate of change of momentum.

$: \implies \sf F = \dfrac{m(v-u)}{t}$

$: \implies \sf F = \dfrac{100 (8-5)}{t}$

$: \implies \sf F = 10 \times \dfrac{3}{6}$

$: \implies \bf F = 50 N$

Therefore,

The magnitude of the force exerted on the body is 50N.