Numerical on Momentum class 9
Last updated on May 12th, 2023 at 01:58 pm
This post is to solve some Numerical on Momentum for class 9. These are numerical problems related to momentum and impulse concepts in physics. Impulse-momentum theorem and Impulse equation help a lot to solve this momentum numerical set.
This set is good for students of class 9 & class 10 (covering grade 9 and grade 10 physics standards of different international boards).
Formulas Used
Momentum = mass x velocity
p = mv
We will use the understanding from the impulse momentum theorem:
The impulse of force = change in momentum.
Mathematically writing in an impulse equation it goes like this:
Ft = mv-mu
[ where, F= force, t = time duration, m = mass of the body. u and v are initial and final velocities respectively.]
Momentum Numericals – Questions and Answers
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:
The 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
The 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