by Patrick Ford

Hey guys, when this problem we're pulling a crate of an inclined planes. I'm just gonna go ahead and draw that real quick about my incline plane like this. I've got my box and I know that the mass is equal to 19 kg. So M equals 19. I'm gonna go ahead and label all the forces that are acting on this crate. I have an applied force that is parallel to the ramp and it's 130 noon. So this FAA here is 130. Now I also have some gravity. Right? So I have this MG here, this is going to be my MG. And I have a normal force like this. Remember that are inclined planes we're gonna separate RMG and we're gonna have an MG. X. That points down the incline like this. And we actually are told that nothing about friction. So we're not gonna do this any friction in this problem. So in the first part here, I want to calculate the work that some of gravity. So the work that is done by MG. Remember that on an inclined plane? The work that's done by MG is the same exact thing. That's the work is done by MG X. This just allows us to simplify our equation and really this is just gonna be MG times the sine of the Theta X. In which data X. Is the angle of the incline here. What's hold? This is 36 degrees. So that's the end. We're gonna plug into this data X. Here. So it's MG. X. Sine theta. Sorry, MG sine Theta X times D. And we've already taken care of that co sign stated term. It's just this right here. Now what we have to do is we have to determine the direction of positive because that's going to influence whether our works are positive or negative now because we're pulling this 19 creates up the ramp. So that means that the displacement over here is actually gonna be this way. So, this distance here we're told is 15 m that I'm gonna choose this direction to be positive. And that means that this work done by gravity is actually gonna be negative. All right. So this is just gonna be negative And I'm just gonna plug it on my numbers. So, I got the mass which is 19 times the 9. times the sine of theta. Which is the sign of 36 times the distance that I'm pulling it over which is 15. Now again, there's no need to put this cosign Theta term here. This coastline between this MG. X. And D. Because the negative sign already takes care of that. I remember that MG. X. Is going to be parallel to displacement. So you actually don't need to do this. All right. So you just plug in all these numbers here. What you're gonna get is negative 1640 jewels. So that's the answer to part a. Alright, makes sense. It's negative because as you're going up the ramp, gravity is going to be doing negative work on you. All right. So, let's go ahead and we want to part B. And part You want to figure the final kinetic energy of the great. We just calculated to work. How do we relate that to kinetic energy? Remember, we just use the work energy theorem. The network on an object which is just the sum of all the works is just equal to the change in the kinetic energy. Now, in this case remember we have three forces we have are applied force, RMG X and the normal force. So when we go to some all of our works, the network is going to be the work done by the applied force. The work done by friction which we just calculated. I'm sorry that that the work of a friction work done by gravity which we just calculated plus the work done by the normal force. Remember the normal force is sort of a perpendicular. Right. It's gonna be pointing sort of in the new y axis, perfectly good to the incline and it's going to be perpendicular to the direction of motion. So there is no work done by the normal force. So it's just these two that contribute works and that's equal to change in the kinetic energy. That's kinetic energy final minus kinetic energy. Initial. We know that we're starting from rest. RV not equal zeros. There is no initial kinetic energy. So really the network, all these works here are gonna be really just do are going to equal the kinetic energy final. So I've already just calculated the W. M. G. In part A. Now all I have to do here is it just have to calculate the work done with the applied force and then I can figure out the kinetic energy final. Whether the applied force is just gonna be F. A. Times D. Co signed data. So that means the work done by the applied force here Is gonna be my apply force of 130 times the distance is 15. And then what about the angle? Well the FAA and the distance are going to be pointing in the same direction. They will be parallel. So this is just going to turn to the coastline of zero which is just one. And so if you plug this in, what you're gonna get is positive 1950 jewels. So now this is 1950 jules. It's positive. It makes sense because it points in direction of motion. Now we're just gonna plug that back into our F. A. So really the work nets, which is really just the W. F. A. Which is my 1950 plus. My work done by gravity, which is negative 16 40 is going to equal the final kinetic energy. So basically what happens is that the kinetic energy final is going to be equal to 310 jewels. And that's your answer. All right. So let's take this one guys, let me know if you have any questions.

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