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$\cdot$ A 128.0 $\mathrm{N}$ carton is pulled up a frictionless baggage rampinclined at $30.0^{\circ}$ above the horizontal by a rope exerting a72.0 $\mathrm{N}$ pull parallel to the ramp's surface. If the carton travels5.20 $\mathrm{m}$ along the surface of the ramp, calculate the work doneon it by (a) the rope, (b) gravity, and (c) the normal force of theramp. (d) What is the net work done on the carton? (e) Sup-pose that the rope is angled at $50.0^{\circ}$ above the horizontal,instead of being parallel to the ramp's surface. How muchwork does the rope do on the carton in this case?

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Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Cornell University

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Lectures

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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Okay, So in this question we have a ramp which is making 30 linger and the really great angle from the horizontal. And then we have the carton and it's been pulled upwards on DH since the direction of the forces parallel to the inclined ramp. So that's why the force and the displacement are on the same direction. Now toe, calculate the work done. We should be using this equation where f parallel to this apparel time. So if parallel is f course, I knw data, find the displacement where this data is nothing but the angle between the displacement and the ah force. So the applied force. If the flight force and the displacement are on the same direction, that means they're the angle between them will be serious, but inflicts other forces this way if the forces this way. So that means there will be an angle between the force and the distress. When so, we'll have to put that angle over here that will get clear when we start solving the parts. So in the first part say that the force and the displacement are in the same direction, which is along the ramp. So that's why we made fire zero and ah, we know that the given forces 72 Newtons. So we take that and then we put Syria as our angle and then the displacement 5.20 meters and they're using those values. We get the work done as 3 70 For Jules Now this plus sign is important because that signifies that the work done and due to the rope is are the work and do the force applied on the rope is positive now for gravity. Hey, we see that the gravity's and collecting downwards, right? So that means that angle between the force and the displacement is this quantity right here. And if we see that quantities, nothing worked. Um, 90 degrees plus 30 degrees over 30 degrees is the angle that it makes. So ah, if we draw a line around here, we see that this angle and this angler are equals, which is 30 degrees. And then this is a perpendicular line because it's horizontal. And then this is the perpendicular, the horizontal. So that's why we add 92 30 to get the angle that ah, that is making that the force due to gravity is making with the displacement. So that's 1 20 degrees. Now again, we'll be using the same question now. Ah, here the forces 1 28 mutants on DH again. We get that by him by doing m times t where Jesus gravitation Force m is the mass and ah, this is the angle that it makes. And then 5.20 is the displacement of the displacement is same. But now we see that the world and is negative. So we get negative 333 jewels. So that means the work done due to gravity is negative and we can actually see are we can actually intuitively say that since the gravity is acting downwards although the box or the carbon is going up. So that's why we see that the force due to gravity is negative now in part. See, we have to find out the world turned you to the normal, of course, So the normal force will be exactly perpendicular to the ram. So that's n. So if this is the force, this is a normal force. That means it's making a 90 degree angle with the displacement. So if I cz 90 now And if we put fires 90 in this. A question. So call. Sign off. FYI, if we said that Tu 90 degrees, that becomes zero. So that's why I worked. And you tow the normal force is zero. And for part of the way, we have to find out the net Force s o the net forces the world done. Sorry, the network work done. So the network turn is the work and you to the rope. Plus that worked. And do tow the gravity and the normal and the world can do to the normal force. And if we add them up, we get 41. Jules. So we're concerning the sign here. And since we saw that we were going to the gravity is negative. So that's why we're technically subtracting one from the other to get this work done? No. And in the final part, we're saying that the flight force is now making an angle 50 degrees from the horizontal. So we know that this part is that really so This is our new force. So we just wanted a new So the angle between the displacement and the new force will be 20 degrees because We know that this whole angle is 15 degrees and bangle between the old force or the displacement to the horizontal is 30 degrees, so we can subtract 50 from 30 toe, get the angle between displacement and the new force. So we did that. And by doing so, we get the anguish 20 degrees. So now we do the same thing. We take the force with the seven to Newman's and then cause I in 20 degrees because the angle is 20 that this was the discretion is the same with five point toe, and that gives us the total work. Dennis 3 52 jurors. So technically, we see that that force, or that Warrenton is lesser than the work done when the rope is ah, paralleled, the applied force is parallel to the displacement, so it's always better toe pull the garden at a certain angle, which is greater than the displacement greater than zero. Thank you

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