What is momentum a car of mass 500 kg is moving with a velocity of 20 m/s calculate its momentum?

Table of Contents Show

Example: What is the momentum of a 1500 kg car going at highway speed of 28 m/s (about 100 km/h or 60 mph)?
Example: You are 60 kg and run at 3 m/s into a wall. The wall stops you in 0.05 s. What is the force? The wall is then padded and stops you in 0.2 s. What is the force?
Impulse From Force
Momentum is Conserved
In our Universe:
Momentum is a Vector
One Dimension
Two or More Dimensions
Example: A pool ball bounces! It hits the edge with a velocity of 8 m/s at 50°, and bounces off at the same speed and reflected angle. It weighs 0.16 kg. What is the change in momentum?

Momentum is how much something wants to keep moving in the same direction.

This truck would be hard to stop ...

... it has a lot of momentum.

Faster? More momentum!
Heavier? More momentum!

Momentum is mass times velocity.
The symbol is p:

p = m v

Example: What is the momentum of a 1500 kg car going at highway speed of 28 m/s (about 100 km/h or 60 mph)?

p = m v

p = 1500 kg × 28 m/s

p = 42,000 kg m/s

The unit for momentum is:

kg m/s (kilogram meter per second), or
N s (Newton second)

They are the same! 1 kg m/s = 1 N s

We will use both here.

More examples:

	Mass	Speed	Momentum
Bullet (9 mm)	7.5 g 0.0075 kg	1000 m/s	0.0075 × 1000 = 7.5 kg m/s
Tennis Ball	57 g 0.057 kg	50 m/s	0.057 × 50 = 2.85 kg m/s
Soccer Ball	16 oz 0.45 kg	100 km/h 28 m/s	0.45 × 28 = 12.6 kg m/s
Basket Ball	22 oz 0.6 kg	3 m/s	0.6 × 3 = 1.8 kg m/s
Hammer	400 g 0.4 kg	7 m/s	0.4 × 7 = 2.8 kg m/s
Runner	80 kg	9 km/h 2.5 m/s	80 × 2.5 = 200 kg m/s
Car	1500 kg	100 km/h 28 m/s	1500 × 28 = 42,000 kg m/s

Momentum has direction: the exact same direction as the velocity.

But many examples here only use speed (velocity without direction) to keep it simple.

Animation

Play with momentum in this animation.

Impulse

Impulse is change in momentum. Δ is the symbol for "change in", so:

Impulse is Δp

Force can be calculated from the change in momentum over time (called the "time rate of change" of momentum):

F = Δp Δt

Example: You are 60 kg and run at 3 m/s into a wall. The wall stops you in 0.05 s. What is the force? The wall is then padded and stops you in 0.2 s. What is the force?

First calculate the impulse:

Δp = m v

Δp = 60 kg x 3 m/s

Δp = 180 kg m/s

Stopping in 0.05 s:

F = Δp Δt

F = 180 kg m/s 0.05 s = 3600 N

Stopping in 0.2 s:

F = Δp Δt

F = 180 kg m/s 0.2 s = 900 N

Stopping at a slower rate has much less force!

And that is why padding works so well
And also why crash helmets save lives
And why cars have crumple zones

Start with:		F = ma
Acceleration is change in velocity v over time t:		F = m Δv Δt
Rearrange to:		F = Δmv Δt
And Δmv is change in momentum:		F = Δp Δt

Impulse From Force

We can rearrange:

F = Δp Δt

Into:

Δp = F Δt

So we can calculate the Impulse (the change in momentum) from force applied for a period of time.

Δp = F Δt

Δp = 300 N × 0.02 s

Δp = 6 N s

Momentum is Conserved

Conserved: the total stays the same (within a closed system).

Closed System: where nothing transfers in or out, and no external force acts on it.

In our Universe:

Mass is conserved (it can change form, be moved around, cut up or joined together, but the total mass stays the same over time)
Energy is conserved (it also can change form, to light, to heat and so on)
And Momentum is also conserved!

Note: At an atomic level Mass and Energy can be converted via E=mc2, but nothing gets lost.

Momentum is a Vector

Momentum is a vector: it has size AND direction.

Sometimes we don't mention the direction, but other times it is important!

One Dimension

A question may have only one dimension, and all we need is positive or negative momentum:

Two or More Dimensions

Questions can be in two (or more) dimensions like this one:

Example: A pool ball bounces! It hits the edge with a velocity of 8 m/s at 50°, and bounces off at the same speed and reflected angle. It weighs 0.16 kg. What is the change in momentum?

Let's break the velocity into x and y parts. Before the bounce:

vx = 8 × cos(50°) ...going along
vy = 8 × sin(50°) ...going up

After the bounce:

vx = 8 × cos(50°) ...going along
vy = 8 × −sin(50°) ...going down

The x-velocity does not change, but the y-velocity changes by:

Δvy = (8+8) × sin(50°)
= 16 × sin(50°)

And the change in momentum is:

Δp = m Δv

Δp = 0.16 kg × 16 × sin(50°) m/s

Δp = 1.961... kg m/s

p = m v
Momentum is mass times velocity

is not the full story!

It is a wonderful and useful formula for normal every day use, but when we look at the atomic scale things don't actually collide. They interact from a distance through electro-magnetic fields.

And the interaction does not need mass, because light (which has no mass) can have momentum.

11985, 17629, 11991, 17630, 17636, 11993, 17635, 17640, 17643, 17648

The conservation of momentum calculator will help you in describing the motion of two colliding objects. Are you wondering what is momentum? Do you want to gain a better understanding of the law of conservation of momentum? Are you perplexed by the concepts of an elastic and inelastic collision? Or maybe you can't tell the difference between kinetic energy and momentum conservation principles? Whatever the reason, this article is here to help you.

Prefer watching rather than reading? Check out our video lesson on conservation of momentum here:

The principle of momentum conservation says that for an isolated system, the sum of the momentums of all objects is constant (it doesn't change). An isolated system is a system of objects (it can be, and typically is, more than one body) that doesn't interact with anything outside the system. In such a system, no momentum disappears: whatever is lost by one object is gained by the other.

Imagine two toy cars on a table. Let's assume they form an isolated system - no external force acts on them, and the table is frictionless. One of the cars moves at a constant speed of 3 km/h and hits the second toy car (that remained stationary), causing it to move. You can observe that the first car visibly slows down after the collision. This result happened because some momentum was transferred from the first car to the second car.

We can distinguish three types of collisions:

Perfectly elastic: In an elastic collision, both momentum and kinetic energy of the system are conserved. Bodies bounce off each other. An excellent example of such a collision is between hard objects, such as marbles or billiard balls.
Partially elastic: In such a collision, momentum is conserved, and bodies move at different speeds, but kinetic energy is not conserved. It does not mean that it disappears, though; some of the energy is utilized to perform work (such as creating heat or deformation). A car crash is an example of a partially elastic collision - metal gets deformed, and some kinetic energy is lost.
Perfectly inelastic: After an inelastic collision, bodies stick together and move at a common speed. Momentum is conserved, but some kinetic energy is lost. For example, when a fast-traveling bullet hits a wooden target, it can get stuck inside the target and keep moving with it.

You may notice that while the law of conservation of momentum is valid in all collisions, the sum of all objects' kinetic energy changes in some cases. The potential energy, however, stays the same (what is in line with the potential energy formula).

You can use our conservation of momentum calculator to consider all cases of collisions. To calculate the velocities of two colliding objects, simply follow these steps:

Enter the masses of the two objects. Let's assume that the first object has a mass of 8 kg, while the second one weighs 4 kg.
Decide how fast the objects are moving before the collision. For example, the first object may move at a speed of 10 m/s, while the second one remains stationary (speed = 0 m/s).
Determine the final velocity of one of the objects. For example, we know that after the collision, the first object will slow down to 4 m/s.
Calculate the momentum of the system before the collision. In this case, initial momentum is equal to 8 kg * 10 m/s + 4 kg * 0 m/s = 80 N·s.
According to the law of conservation of momentum, total momentum must be conserved. The final momentum of the first object is equal to 8 kg * 4 m/s = 32 N·s. To ensure no losses, the second object must have momentum equal to 80 N·s - 32 N·s = 48 N·s, so its speed is equal to 48 Ns / 4 kg = 12 m/s.
You can also open the advanced mode to see how the system's kinetic energy changed and determine whether the collision was elastic, partially elastic, or inelastic.

According to the principle of conservation of momentum, the total linear momentum of an isolated system, i.e., a system for which the net external force is zero, is constant.

In order to conserve momentum, there should be no net external force acting on the system. If the net external force is not zero, momentum is not conserved.

The recoil of a gun when we fire a bullet from it is an example of conservation of momentum. Both the bullet and the gun are at rest before the bullet is fired. When the bullet is fired, it moves in the forward direction. The gun moves in the backward direction to conserve the total momentum of the system.

The principle that makes a rocket move is the law of conservation of linear momentum. The fuel burnt in the rocket produces hot gas. The hot gas is ejected from the exhaust nozzle and goes in one direction. The rocket goes in the opposite direction to conserve momentum.