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
Find the reading of the spring balance shown in the following figure. The elevator is going up with an acceleration g/10, the pulley and the string are light and the pulley is smooth.
An empty plastic box of mass m is found to accelerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?
A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s2. Find the displacement of the block during the first 0.2 s after the start. Take g = 10 m/s2.
Use Newton's second law of motion to explain the following instance :
A cricketer pulls his hands back while catching a fast moving cricket ball .
The linear momentum of a ball of mass 50 g is 0.5 kg m s-1. Find its velocity.
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : The velocity acquired by the body
A motorcycle of mass 100 kg is running at 10 ms−1. If its engine develops an extra linear momentum of 2000 Ns, calculate the new velocity of a motorcycle.
State two factors which determine the momentum of a body.
Define Newton’s second law of motion.
Use Newton's second law to explain the following:
We always prefer to land on sand instead of hard floor while taking a high jump.
