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.

**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? **

** 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.**

**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,

P_{before collision }= P_{after collision}

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

Where m_{1}u_{1} is the momentum of the 1st object and m_{2}u_{2} is the momentum of the 2nd object before the collision.

Where m_{1}v_{1} is the momentum of the 1st object and m_{2}v_{2 }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.

m_{1}u_{1} + m_{2}u_{2} = 0

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

P_{before collision} = m_{1}u_{1} + m_{2}u_{2}

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

P_{before collision }= m_{1}u_{1} + (-m_{2}u_{2})

P_{before collision }= m_{1}u_{1} – m_{2}u_{2}

**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**:

m_{1} =15kg

m_{2} = 10kg

u_{1} = 25m/s

u_{2 }= 20m/s

** To Find**:

P_{before collision }when both objects move in the same direction =?

P_{before collision }when both objects move in the opposite direction =?

** Formula**:

P_{before collision }= m_{1}u_{1} + m_{2}u_{2}

P_{before collision }= m_{1}u_{1} – m_{2}u_{2}

** Solution**:

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

P_{before collision }= m_{1}u_{1} + m_{2}u_{2}

Substituting all values,

P_{before collision }= 15 x 25 + 10 x 20

P_{before collision }= 375 + 200

P_{before 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**,

P_{before collision }= m_{1}u_{1} – m_{2}u_{2}

Substituting all values,

P_{before collision }= 10 x 20 – 15 x 25

P_{before 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. **

As per **law of conservation of energy**,

K.E_{before collision }= K.E_{after collision}

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

m_{1}u_{1} + m_{2}u_{2} = 0

P_{before collision }= m_{1}u_{1} + m_{2}u_{2}

Therefore, the total kinetic energy after collision K.E_{after collision} is also zero.

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

K.E_{before collision }=(1/2)m_{1}u_{1}^{2}+(1/2) m_{2}u_{2}^{2}

**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**:

m_{1} = 5kg

m_{2} = 3kg

u_{1} = 10m/s

u_{2} = 12m/s

** To Find**:

P_{before collision }=?

KE_{before collision }=?

** Formula**:

P_{before collision }= m_{1}u_{1} + m_{2}u_{2}

K.E_{before collision }= (1/2)m_{1}u_{1}^{2}+(1/2) m_{2}u_{2}^{2}

** Solution**:

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

P_{before collision }= m_{1}u_{1} + m_{2}u_{2}

Substituting all values,

P_{before collision }= 5 x 10 + 3 x 12

P_{before collision }= 50 + 72

P_{before 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.E_{before collision }= (1/2)m_{1}u_{1}^{2}+(1/2) m_{2}u_{2}^{2}

Substituting all values,

K.E_{before collision }= (1/2)*5*10^{2}+(1/2)*3*12^{2}

K.E_{before collision }= (500/2)+(432/2)

K.E_{before collision }= 250 + 216

K.E_{before 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,

P_{before collision }= m_{1}u_{1} + m_{2}u_{2}

**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. **

** Given**:

m_{1} = 5kg

m_{2} = 6kg

m_{3} = 4kg

u_{1} = 8m/s

u_{2} = 12m/s

u_{3} = 17m/s

** To Find**: P

_{before coliision }=?

** Formula**:

P_{before collision }= m_{1}u_{1} + m_{2}u_{2} – m_{3}u_{3}

** Solution**:

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

P_{before collision }= m_{1}u_{1} + m_{2}u_{2} – m_{3}u_{3}

Substituting all values,

P_{before collision }= 5 x 8 + 6 x 12 – 4 x 17

P_{before collision }= 40 + 72 – 68

P_{before collision }= 112 – 68

P_{before collision }= 44

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