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.
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.
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.
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.
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?
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
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
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