# Practice Applying Linear Momentum Formulas

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• 1:53 Linear Momentum Problems
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Lesson Transcript
Instructor: Matthew Bergstresser
Momentum is product of mass and velocity, and it is a quantity that is always conserved in collisions. In this lesson, we will dig deep into the concept of linear momentum, including practice working momentum problems.

## Linear Momentum

The Civil War battlefield museum in Petersburg, Virginia, has an artifact that was found on the battlefield. It is two bullets that fused together after colliding head on during the battle. Imagine that! Two bullets collided head-on. What are the chances of that happening? This battle occurred over 150 years ago, but with our physics knowledge, we can reconstruct what happened with these two bullets on that fateful day.

Momentum is the product of an object's mass and velocity and is a vector, so we have to be very careful with directions of momentum. The equation for momentum is:

• p is momentum in kilogram-meter-per-second (kgm/s)
• m is mass in kilograms (kg)
• v is velocity in meters-per-second (m/s)

Many students ask how to know what approach or equations should be used when dealing with a physics problem. There are buzz words to look for to help know which approach to take. When the words ''collision'', ''collide'', or ''explodes'' are used, think about momentum. Momentum is always conserved unless there are external forces acting on the system.

The center-of-mass approach to solving momentum problems is extremely powerful because it allows you to calculate final velocities without getting tangled up with kinetic energy, which is conserved in elastic collisions, but not conserved in inelastic collisions.

Elastic collisions occur when objects collide and then bounce off of each other. Think of pool balls colliding. This isn't perfectly elastic, but it makes the point. Inelastic collisions occur when objects collide, stick together, and move as one mass. Let's go through some examples of linear momentum problems.

## Linear Momentum Problems

• A 5 kg mass is sliding on a friction-less surface at 0.5 m/s. It collides with, and sticks to, a 1 kg mass at rest. Determine the final velocity of the combination mass.

Drawing a sketch of the scenario always helps to visualize the scenario, including the relevant numbers needed.

This is a classic inelastic collision, because the two masses stick together after the collision and move together afterwards. We will use the momentum equation to solve for the final velocity, keeping in mind that momentum is always conserved. The subscripts on the masses are the mass values.

So, the final velocity of both masses is 0.4m/s.

• Two bullets have the same mass, 0.02 kg, and they are moving horizontally directly at each other at 280 m/s. They hit head-on and stick together. What is their combined velocity the instant after they collide?

This problem requires us to use unit-vector notation to indicate the velocities of the bullets because they are not moving in the same direction. As in the last problem, we first draw a sketch.

The velocity right after the collision is zero, in the î direction. You might be wondering how this can be correct since the bullet combination didn't stay frozen in the air. It fell to the ground. This is where the external force comes into play, which is gravity in this case. The mass of metal fell straight to the ground.

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