 ###### Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

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# Impulse

Matt Jones ###### Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

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Impulse measures the change in the momentum of an object. Impulse is expressed as the integral of force over time and its unit is the Newton-second (N x s). Expressed without Calculus, impulse = force x time.

Impulse, impulse is the change in momentum caused my force applied over time and remember change in momentum we can use the delta triangle to symbolize the change and momentum is simply mass times velocity or kilograms times meters per second. Okay so the force times time it's the impulse, that's the impulse that causes that change in momentum. Some examples of this, if I take a plate and I drop it on a concrete floor it's going to shutter. If I take that same plate and drop it it's going to have the same momentum but if it hits a carpet at floor it's probably not going to break and that's because the time on there is going to be greater. It's going to actually absorb that plate a little bit as it sinks into the carpet and though the change in overall momentum is the same it's going to end up with 0 momentum at the end. The amount of time it takes to stop it is reduced so the plate doesn't shatter.

Same thing is if a person jumps out of a window into a swimming pool their momentum is the same and the water is going to stop their momentum if they jump out of the same window onto a concrete side walk their momentum is going to be stopped instantly t is going to be very small as their instantaneously stopped and they're going to get hurt right, they're really going to get hurt in that case. So that's an example of the same impulse changing momentum but because the time is different it's going to affect the net force that's applied to change that impulse okay. Let's look at some examples of calculating an impulse, and then using that impulse to calculate the change in momentum. Okay I've got a force of 30 Newtons exerted for 4 seconds on a 90 kilogram object. What's the impulse applied?

Okay so again the change in momentum here equals force in Newtons times time in seconds okay and I've got 30 Newtons times 4 seconds and that's going to equal 120 Newton seconds which is in the unit for an impulse okay. So if the impulse is 120 Newton seconds then that's also the change in momentum okay so the change in momentum is the same 120 Newton seconds. Okay, so that's pretty straight forward, now if I know the change in momentum I can calculate the change in velocity. Because remember the momentum is the mass times the velocity so if I say 120 Newton seconds equals in this case 90 kilograms is the mass and the velocity is what we're trying to solve for v. Okay, so to simplify that I can take my 90 kilogram v divided by 90 kilogram and that's going to equal 120 Newton seconds divided by 90 kilogram okay.

Now the units here remember, what is a Newton? A Newton is a mass applied over a distance meters per second squared okay. So if I convert my Newton to that okay notice I've got now, I've got seconds squared over here and I've got a second so I can cancel that with one of those and I can cancel my kilograms with that I cancel out this unit completely and my velocity here equals again 90 divided by I'm sorry 120 divided by 90 and then the only thing I've left here is meters per second so 1.33 meters per second. So I've calculated the velocity based on the change in momentum and that's how we can solve problems related to impulse.