Sarah Allen - Momentum - Stick Figure Physics 3

Welcome to this tutorial on momentum; this guide covers the basics of calculations involved in collision problems.

If you get confused while working on it, please email me at SarahAllenPhysics@gmail.com

so I can improve it!

Or, say hello on my website: StickFigurePhysicsTutorials.com.

Momentum is the mass times the velocity of an object. Its useful because, happily, it never changes. Things bounce off one another, but the total momentum stays the same (as long as no outside forces push things around.)

This means that we can use momentum to figure out how fast objects are travelling before or after collisions or explosions.

Momentum is a vector (meaning it is not just an amount but also a direction.)

This is the equation for momentum: (P stands for momentum, m stands for mass, and v stands for velocity.)

Here are the units of mass and velocity: (m stands for meters, s for seconds, and kg for kilograms.)

So, the units of momentum are:

But, they are usually written as

(Newton- seconds)

Why are these the same? Well, a Newton is a unit of force, and

So,

So, a Newton is a kg*m/s2. Which means that a Newton times a second is

Which is what we had before!

Momentum is a vector, and this affects how you work with it. A vector has both magnitude (the total amount of momentum,) and direction (the direction the object is moving.)

All this means is that if you are adding up momentums to get a total amount of momentum, you have to pay attention to their directions:

Try This: What is the total momentum if a 10kg ball is travelling East at 20 m/s and a 5 kg ball is travelling West at 8 m/s?

Check Your Answer:

This gets a little more complicated if the momentum vectors are at more complicated angles.

Sometimes they are at right angles to one another:

Start by writing them tip to tail, which means put the tail of one vector at the tip of the other:

The resultant vector starts at the tail of one, and ends at the tip of the other:

Simply use the Pythagorean Theorem to get the magnitude:

And the inverse tangent to get the angle:

If one or both of the vectors is at a weird angle, just break each of the vectors into their horizontal and vertical components.

Lets say we wanted to add these:

Break them into components (using SOH CAH TOA):

To get the x component of the resultant vector, add the x components:

To get the y component of the resultant vector, add the y components. (These are pointing in opposite directions, though, so well subtract.):

(The result is negative, which means that, because the one that was pointing down was negative, our y component also points down.) Heres the resultant vector:

Try finding the magnitude and direction of the resultant vector above.

Check your Answer:

Try this: A car with a mass of 1,000 kg is driving North with a velocity of 30 m/s. Another car is driving at an angle of 45 degrees East of North. It has a mass of 1500 kg and a velocity of 15 m/s. What is the total momentum of this two-car system?

Check your Answer:

First, find their momentums:

Then, find the x and y components of their momentums:

Add the x components:

0 + 15910 = 15910

Add the y components:

30000 + 15910 = 45910

Find the magnitude and direction of the resultant:

There are two main types of collisions: Elastic and Inelastic.

Its a little counter-intuitive. Elastic collisions are collisions in which the things bouncing off one another dont deform at all. They just bounce right off one another, and the total kinetic energy is conserved. Pool balls are a common example.