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Rutgers, The State University of New Jersey
(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s$^2$ ?
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welcome to our third example video Looking at kinetic energy in this video, we're going to consider the use of plots. Say we have F versus X. In this case, we know that we have the relationship and a girl of FDX is equal to a change in kinetic energy. So if we were to draw a picture that looks something like this yeah, so it goes out to 10 m Say it goes up to 10. Newtons will say that our object has a mass equal to 1 kg that is receiving this force. Eso What can we do here? Well, we know that we have the integral of F d X is equal to Delta K. Let's say that Vienna equals 0 m per second and I want to know what is my V final for this object going to be after this variable force is applied to it? Well, uh, looking at it, let's just take the area under the curve. We find that Delta K, then it's going to be equal to here. We have one half base times height, so that's one half bases 2 m. Hi is 10 Newtons. Plus I got a rectangle here. So that's gonna be 8 m. Times 10 Newtons, check the units. We have kilograms meters per second squared, multiplied by meters. So that's kilograms Meters squared per second squared. That is definitely jewels. And then we say, Okay, well, this is 10. This is 80. So templates, 80 is 90 and we know that Vienna is zero. Therefore, we have one half m. The final squared is equal to 90 Jules solving. Then we find that 180 Jules divided by 1 kg square root of that is going to be equal to our final velocity for this object. So looking at this, then it didn't take many steps and it looked a lot like things we've done in the past where we've taken areas under the curve. Except it was F versus X instead of a versus tea or V versus tea or something like that. We have force versus position. And so we're able to track all this and again. This is because of the meters that we have for calculate for measuring force. We could attach one of those to a computer and it could generate for us Ah, plot like this that we could then use to predict what the final velocity of an object is, or even what the initial ob velocity of the object is. If we went in the opposite direction, saying it started with some velocity and then we'll slowed down by a force, if that were to happen, we would need a negative force here.
Equilibrium and Elasticity
Moment, Impulse, and Collisions
Rotation of Rigid Bodies