Momentum numerical problems – solved (class 9 & class 10 physics)

This post is to solve some numerical problems related to momentum and impulse concepts in physics. This set is good for students of class 9 & class 10 (covering grade 9 and grade 10 physics standards of different boards).

We will use this understanding from the impulse momentum theorem: Impulse of force = change in momentum.

Mathematically writing in an impulse equation or formula form it goes like this:
Ft = mv-mu [ F= force, t = time duration, m = mass of the body. u and v are initial and final velocity respectively.]

Momentum problems – solved using impulse equation | worksheet with solution

1 ] A car of mass 600 kg is moving at 15 m/s. Calculate its momentum.

Solution:
momentum = mass x velocity = 600 kg x 15 m/s = 9000 kg m/s

2 ] The driver accelerates gently so that a force of 30 N acts on the car for 10 seconds. Calculate the impulse of the force.

Solution:
Impulse of the force = Force x time duration = 30 x 10 N s = 300 Ns.

3 ] A car of mass 500 kg is moving at 20 m/s. Calculate its initial momentum. The driver accelerates gently so that a force of 50 N acts on the car for 8 seconds. Calculate the final momentum.

Solution:
Initial momentum = mass x initial velocity = 500 x 20 kg m/s = 10000 kg m/s
Impulse of the force applied = force x time duration = 50 x 8 Ns = 400 Ns
We know that the impulse of force = change of momentum
The car had an acceleration, so the final momentum = initial momentum + impulse of force = (10000 + 400) kg m/s =10400 kg m/s

4 ] Calculate the momentum of a car of mass 600 kg moving at 30 m/s.

Solution:

Momentum = mass x velocity = 600 x 30 kg m/s = 18000 kg m/s

5 ] A force of 20 N acts on a rocket for 250 seconds, causing the rocket’s velocity to increase
a) Calculate the impulse of the force
b) By how much does the rocket’s momentum increase?


Solution:
a) The impulse of the force = force x time = 20 x 250 Ns = 5000 N s.

b) We know, the impulse of the force = change in momentum,
As here, the rocket’s velocity increases, therefore the rocket’s momentum increases.

And, the Rocket’s momentum increase = impulse of the force applied = 5000 kg m/s.

6] A 10 kg body is moving with a constant acceleration of 4 m/s^2. If the initial velocity of the body is 2 m/s, what is the change in momentum in 5 s?

Mass of the body (m)= 10kg
Acceleration of the body(a)= 4m/s^2
Initial velocity of the body (u)=2m/s
Change in momentum after time t=5s
(∆p)=?

Solution:

Method 1

Final velocity: v = u + at

v = 2 + 4 × 5

v = 2 + 20

v = 22m/s

Change in momentum = ∆p= m × v — m × u

∆p = 10 × 22 — 10 × 2

∆p = 220 — 20

∆p = 200 kg.m/s

Ans) The change in momentum of a body is 200kg.m/s

Method 2

F = m×a

F = 10 × 4

F = 40N

Using the formula: F = ∆p/t

∆p = F × t

∆p = 40N × 5s

∆p = 200Ns = 200 kgm/s^2 × s = 200 kg.m/s

Ans) The change in momentum of a body is 200 kg.m/s

Related Study:

Impulse

Impulse momentum Theorem


Momentum numerical problems – solved (class 9 & class 10 physics)
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