How to Calculate Momentum Before Collision: Elastic, Inelastic, Formula and Problems


The article discusses about how to calculate momentum before collision with its formulas and problems. 

The momentum before the collision is estimated as carrying a product of mass and velocity. Before the collision, there is no external force to change the motion. So, an object having mass at rest is stated to be having zero momentum, or an object is a motion stated to be moving with momentum. 

An object’s momentum before collision is given by P = mv. 

In the absence of external force, its motion and momentum do not vary before the collision. 

Read more about Momentum.

What is the momentum of a car having a mass of 60kg moving with a high speed of 120km/hr before the collision with other vehicles? 

How to Calculate Momentum Before Collision
How to Calculate Momentum Before Collision

Given:

m = 60kg

v = 120km/hr

v = 120 x 1000/3600 m/s

To Find: P =?

Formula:

P = mv

Solution:

The momentum of car before collision is calculated as,

P = mv

Substituting all values

P = 60 x 120 x 1000/3600

P = 7200000/3600

P = 2000

The car’s momentum before collision is 2000 kg.m/s.

Car accident due to High Momentum
Collision due to High Momentum
Go with Low Momentum.. Drive Safe
(credit: shutterstock)

How to Find Total Momentum of Two Objects Before Collision?

The total momentum of two objects before collision is calculated using the conservation of momentum. 

When two objects with different masses and velocities collide, their individual momentum may change. Still, their total momentum stays the same as per the law of conservation of momentum. So, before the collision, we calculate the momentum of two objects by adding their individual momentum. 

The conservation of momentum says,

Pbefore collision = Pafter collision

m1u1 + m2u2 = m1v1 + m2v2

Where m1u1 is the momentum of the 1st object and m2u2 is the momentum of the 2nd object before the collision.  

Where m1v1 is the momentum of the 1st object and m2v2 is the momentum of the 2nd object after the collision.  

When we desire to calculate the total momentum of two objects before the collision, their total momentum after collision is zero. 

m1u1 + m2u2 = 0 

When two objects move in the exact direction, the total momentum before the collision is, 

Pbefore collision = m1u1 + m2u2

When two objects move in opposite directions, the total momentum before the collision is, 

Pbefore collision = m1u1 + (-m2u2)

Pbefore collision = m1u1 – m2u2

Total Momentum Before Collision
Total Momentum of Two Objects Before Collision

Read more about Momentum after Collision.

Suppose an object has a mass of 10kg moving at 20m/s and another object having a mass of 15kg moving at 25 m/s before the collision.  

i) Calculate the total momentum of two objects before collision when both objects move in the same direction. ii) Calculate the total momentum of two objects before collision when both objects move in the opposite directions. 

Given:

m1 =15kg

m2 = 10kg

u1 = 25m/s

u2 = 20m/s

To Find:

Pbefore collision when both objects move in the same direction =?

Pbefore collision when both objects move in the opposite direction =?

Formula:

Pbefore collision = m1u1 + m2u2

Pbefore collision = m1u1 – m2u2

Solution:

i) Total momentum before collision when both objects move in same direction using the law of conservation of momentum,

Pbefore collision = m1u1 + m2u2

Substituting all values,

Pbefore collision = 15 x 25 + 10 x 20

Pbefore collision = 375 + 200

Pbefore collision = 575

Total momentum before collision when both objects move in the same direction is 575kg.m/s

ii) Total momentum before collision when both objects move in the opposite direction using the law of conservation of momentum,

Pbefore collision = m1u1 – m2u2

Substituting all values,

Pbefore collision = 10 x 20 – 15 x 25

Pbefore collision = 175

Total momentum before collision when both objects move in the opposite directions is 175kg.m/s

How to Calculate Momentum Before Elastic Collision

The momentum before elastic collision is calculated using the conservation of energy. 

When two objects having different masses and velocities elastically collide with each other, their individual kinetic energies may get changed. Still, their total kinetic energy remains the same as per the law of conservation of energy. So, before the elastic collision, we calculate the total energy of two objects by adding their kinetic energies. 

Momentum Before Collision
How to Calculate Momentum Before Elastic and Inelastic Collision
(credit: shutterstock)

As per law of conservation of energy

K.Ebefore collision = K.Eafter collision

When we want to calculate the momentum of two objects before elastic collision, their total momentum after elastic collision Pafter collision is zero. 

m1u1 + m2u2 = 0 

Pbefore collision = m1u1 + m2u2

Therefore, the total kinetic energy after collision K.Eafter collision is also zero.

Therefore, the total momentum of two object before collision is,

K.Ebefore collision =(1/2)m1u12+(1/2) m2u22

Read more about Kinetic Energy.

Suppose two balls have masses 5kg and 3kg moving in the same direction at 10m/s and 12m/s colliding elastically. 

i) What is the total momentum before the elastic collision? ii) What is the total kinetic energy before the elastic collision? 

Given:

m1 = 5kg

m2 = 3kg

u1 = 10m/s

u2 = 12m/s

To Find:

Pbefore collision =?

KEbefore collision =?

Formula:

Pbefore collision = m1u1 + m2u2

K.Ebefore collision = (1/2)m1u12+(1/2) m2u22

Solution:

i)The total momentum of balls before the elastic collision is calculated using the conservation of momentum.

Pbefore collision = m1u1 + m2u2

Substituting all values,

Pbefore collision = 5 x 10 + 3 x 12

Pbefore collision = 50 + 72

Pbefore collision = 122

The total momentum of balls before the elastic collision is 122kg.m/s.

ii)The total kinetic energy before the elastic collision is calculated using the conservation of energy.

K.Ebefore collision = (1/2)m1u12+(1/2) m2u22

Substituting all values,

K.Ebefore collision = (1/2)*5*102+(1/2)*3*122

K.Ebefore collision = (500/2)+(432/2)

K.Ebefore collision = 250 + 216

K.Ebefore collision = 466

The total kinetic energy before the elastic collision is 466J.

How to Calculate Momentum before Inelastic Collision?

The momentum before inelastic collision is calculated using the conservation of momentum. 

The total kinetic energy of objects changes after the inelastic collision. Therefore, the energy is not conserved in an inelastic collision. But we can calculate total momentum before inelastic collision by adding their individual momentums using conservation of momentum. 

The total momentum before the inelastic collision is given as,

Pbefore collision = m1u1 + m2u2

Read more about Speed.

Suppose three pool balls have masses 5kg, 6kg, and 4kg moving at 8m/s, 12m/s, and 17 m/s, respectively. Before the inelastic collision of all three balls, calculate the total momentum when two balls move in the same direction and the third ball moves the opposite direction. 

Calculating Total Momentum of Pool Balls
Calculating Total Momentum of Pool Balls (credit: shutterstock)

Given:

m1 = 5kg

m2 = 6kg

m3 = 4kg

u1 = 8m/s

u2 = 12m/s

u3 = 17m/s

To Find: Pbefore coliision =?

Formula:

Pbefore collision = m1u1 + m2u2 – m3u3

Solution:

The total momentum of three pool balls before inelastic collision is calculated using conservation of momentum.

Pbefore collision = m1u1 + m2u2 – m3u3

Substituting all values,

Pbefore collision = 5 x 8 + 6 x 12 – 4 x 17

Pbefore collision = 40 + 72 – 68

Pbefore collision = 112 – 68

Pbefore collision = 44

The total momentum of three pool balls before inelastic collision is 44kg.m/s.


Manish Naik

Hello, I'm Manish Naik completed my MSc Physics with Solid-State Electronics as a specialization. I have three years of experience in Article Writing on Physics subject. Writing, which aimed to provide accurate information to all readers, from beginners and experts. In my leisure time, I love to spend my time in nature or visiting historical places. I am honoured to be part of LambdaGeeks. Looking forward to connecting you through LinkedIn - https://www.linkedin.com/in/manish-ashok-naik/ Also, for Maharashtra travel guide and heritage conservation articles, visit my website Wandering Maharashtra - https://wanderingmaharashtra.com/travel-blogs/

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