To understand how a change in momentum affects an object, we look to impulse. In this lesson, you'll understand how impulse describes an object's change in momentum, as well as how changing the force or time of the impulse can have very different outcomes.
Impulse Affects Momentum
Any moving object can have momentum. This is because momentum is mass in motion. The way we determine an object's momentum is fairly straightforward. Momentum is the object's mass times its velocity, or, in equation form, p=mv, where p is momentum, m is mass in kilograms, and v is velocity in meters per second. Momentum is proportional to both mass and velocity, meaning that a change in one will cause the same amount of change in the other. So if you increase an object's mass, you also increase its momentum. The same is true for velocity: increase or decrease the object's speed, and you increase or decrease its momentum by the same amount.
But usually it's the object's velocity that changes instead of its mass, right? You may remember that a change in velocity means the object is accelerating. You may also remember that acceleration is caused by a force and that the greater the force, the greater the acceleration. Therefore, the greater the acceleration, the greater the momentum!
Force is an important factor, but time also counts. Specifically, when we are interested in knowing how long the force acts. For example, if you push a box across the floor for just a few seconds, the time interval is very short. But if you push a box across the floor and you do so with the same force as before, but this time for several minutes, you've increased the amount of time the force acts. This longer time interval leads to a greater change in momentum. This change in momentum is called impulse, and it describes the quantity that we just saw: the force times the time interval it acts over. The greater the impulse, the greater the change in momentum. To change the impulse, you can either change the amount of force, or you can change the time interval in which that force acts. In equation form, we can write this relationship between impulse and momentum as:
Equation representing relationship between impulse and momentum
The Greek letter delta means 'change in,' and we read this equation as force times the time interval equals change in mass times velocity. Be careful not to read this as 'force times time equals mass times velocity' because now you're saying that 'impulse equals momentum.' It's important to remember that impulse is a change in momentum, not momentum itself.
Changing Time and Force
If you want a large increase in momentum, you need to exert a large force over a long time period. When you quickly shove the box, it doesn't move very quickly across the floor, but if you push it with that same force for a long period of time, you can move it all the way across the room. This is because you've increased the time variable on the left side of the equation. When an object is brought to rest, its momentum also changes, but now it decreases instead of increases. Time is especially important in this situation because a longer time interval means less force acts on the object to result in the same change in momentum.
Say for example that a stunt double jumped from a 10-story window during an action scene. Does she want to land on the sidewalk, which is very hard, or does she want to land on a soft cushion? She definitely wants to land on the soft cushion because this cushioning will increase the time of her impact and decrease the force on her as she lands. In either case, her impulse, or her change in momentum, is exactly the same because in either case, she goes from moving to a state of rest. The difference is that the change occurs over a different time period and with a different amount of force.
If you are stuck in a runaway semi-truck, do you want it to stop by running into a brick wall or running into a pile of dirt? I'll take the dirt any day because the wall causes a change in momentum over a short period of time while the dirt allows the truck to come to a stop more slowly. The force on the truck is much greater as it hits the wall because the time is shorter. Again, in either case, the impulse, or the change is momentum, is exactly the same because both trucks come to a stop. It just occurs over a different time period so the force is different.
This is the same reason that bungee jumpers have such long cords attached to them. If the jumper leaps off the bridge attached to a short cord, he would have the same impulse, or change in momentum, as if he jumped with a long cord. The difference is the force on the jumper. With a short cord, the time interval is decreased so the force on him is increased. With a longer cord, his impulse is spread out over a longer time period, so he can safely dive off the bridge and enjoy the ride.
Momentum is mass in motion, and any moving object can have momentum. An object's change in momentum is equal to its impulse. Impulse is a quantity of force times the time interval. Impulse is not equal to momentum itself; rather, it's the increase or decrease of an object's momentum.
We express momentum as p=mv, where p is momentum, m is mass in kilograms, and v is velocity in meters per second. Impulse is expressed as Ft=delta mv, where F is the force, t is the time interval, and the Greek letter delta means 'change in.'
When an object's momentum decreases, maximizing the amount of time over which that change occurs will result in less force on the object. Falling from a building will hurt a lot less if you could land on a cushioned surface because that cushion extends the time of your fall, decreasing the force. As you decrease the time of the impulse, the force increases. Running a truck into a brick wall will hurt a lot more than running into a pile of dirt because the time of impact is a lot shorter, which means a greater force. In both cases, the same impulse, or change in momentum, occurs. The semi-truck is brought to rest in both cases, but in one situation, that change is quick and painful, while the other situation allows for a slow, gradual change in momentum to occur.
After you have finished with this lesson, you should be able to:
- Define momentum and impulse
- Identify the formulas for momentum and impulse
- Describe real-life examples that explain the relationship between force, momentum and impulse