Advertisements
Advertisements
Question
Show that the rate of change of momentum = mass × acceleration. Under what condition does this relation hold?
Advertisements
Solution 1
Let a force 'F' be applied on a body of mass m for a time 't' due to which its velocity changes from u to v. Then,
Initial momentum of body = mu
Final momentum of body = mv
Change in momentum of the body in 't' seconds = mv - mu = m (v - u)
Rate of change of momentum = Change in momentum/time
= [m (v - u)]/t
However, acceleration a = Change in velocity/time = (v - u)/t
Therefore, rate of change of momentum = ma = mass × acceleration
This relation holds true when the mass of the body remains constant.
Solution 2
According to newton second law
F = m X a
a= (v - u)/t.
F = m(v -u)/t
F = (mv - mu)/t
As F= m X a
ma = (mv - mu)/t
so rate of change of momentum = mass X acceleration.
This relation holds good when mass remains constant during motion.
RELATED QUESTIONS
Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to
- A,
- B along the direction of string. What is the tension in the string in each case?
Suppose you are running fast in a field and suddenly find a snake in front of you. You stop quickly. Which force is responsible for your deceleration?
A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the following figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth h.
A body of mass 5 kg is moving with velocity 2 m s-1. Calculate its linear momentum.
Calculate the magnitude of force which when applied on a body of mass 0.5 kg produces an acceleration of 5 m s-2.
A bullet of mass 50 g moving with an initial velocity 100 m s-1 strikes a wooden block and comes to rest after penetrating a distance 2 cm in it. Calculate: (i) Initial momentum of the bullet, (ii) Final momentum of the bullet, (iii) Retardation caused by the wooden block and (iv) Resistive force exerted by the wooden block.
How long will a stone take to fall to the ground from the top of a building 80 m high
Calculate the velocity of a body of mass 0.5 kg, when it has a linear momentum of 5 Ns.
A stone is thrown vertically upward with a velocity of 9.8 m/s. When will it reach the ground?
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
