In view of the coronavirus pandemic, we are making LIVE CLASSES and VIDEO CLASSES completely FREE to prevent interruption in studies
Physics > Force and Laws of Motion > Momentum and Its Conservation
Force and Laws of Motion

Momentum and Its Conservation

Let’s suppose a speeding truck hits a stationary car due to which the car starts moving. What is actually happening behind the scene? Well here, as the velocity of the truck decreases, the velocity of the car increases and hence the momentum lost by truck is gained by car. Interesting? Let’s find out more about the momentum and its conversation below:

Suggested Videos

Play
Play
Arrow
Arrow
ArrowArrow
Balanced and Unbalanced Forces
Newton's laws
Slider

What is Momentum?

A vector quantity that is the product of the mass and velocity of an object or particle is ‘momentum’. Momentum is measured in the standard unit of kilogram-meter per second (kg · m/s or kg · m · s -1 ). The direction of momentum can be expressed in various ways, depending on the number of dimensions involved. The direction of momentum is same as the direction of velocity.

Momentum, like velocity, is relative. Let us take a 1,000-kg car moving at 20 m/s with respect to the surface of a highway, travelling northward. If the car is driven, the momentum of the car is relative to the body of the person driving the car which is zero. And if a person stands by the side of the road, the momentum of the car relative to that person is 20,000 kg · m/s northward.

Browse more Topics under Force And Laws Of Motion

Linear Momentum

Linear momentum is defined as a vector quantity that is the product of the mass of an object and its velocity. Any change in the mass or the velocity of the system causes a change in linear momentum.

Conservation of Momentum

Momentum

The momentum of a system is constant if there is no external force acting on the system. For a collision occurring between two objects in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

Derivation of Conservation of Momentum

Let us consider a situation wherein: a truck of mass m1, velocity u1 and its momentum = m1u1 and a car of mass m2, velocity u2 and its momentum m2u2; are moving in the same direction but with different speeds. Therefore, total momentum=m1u1 + m2u2.

Now suppose the car and truck collide for a short time t, their velocities will change. So now the velocity of the truck and car become v1 and v2 respectively. However, their mass remains the same. Hence, now the total momentum = m1v+ m2v2

Acceleration of car (a) = (v2–u2)/t

Also, F = ma

F1  = Force exerted by truck on the car

F1 = m2(v2–u2)/t

Acceleration of truck =(v1–u1)/t

F =   m1(v1–u1)/t and F= –F2

m2(v2– u2)/t = –m1(v1– u1)/t

m2v2–m2u= –m1v1+m1u1

or m1u1+m2u = m2v2+m1v1

Solved Example For You

Q. A shell is fired from a gun with a velocity of 300 m/s making an angle 60o with the horizontal. It explodes into two fragments when it reaches the highest position. The ratio of the masses of the two pieces is 1 : 3. If the smaller piece stops immediately after the collision. Find the velocity of the other.

Sol:  Velocity at the highest point = \( 300 \times \cos{60^o} \)

=150 m/s

Using momentum conservation,

\( 150 \times m = 3m/4 \times v \)

\( \Rightarrow v=200 m/s \)

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

Browse

Force and Laws of Motion

2
Leave a Reply

avatar
2 Comment threads
0 Thread replies
0 Followers
 
Most reacted comment
Hottest comment thread
1 Comment authors
Sahil Recent comment authors
  Subscribe  
newest oldest most voted
Notify of
Sahil
Guest
Sahil

Very beautiful explanation

Sahil
Guest
Sahil

Very awesome explantion i found this in many website but this website is good for me.

Browse

Force and Laws of Motion

Stuck with a

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.

Download the App

Watch lectures, practise questions and take tests on the go.

Customize your course in 30 seconds

Which class are you in?
No thanks.