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(II) $\mathrm{A} 75$ -kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a $23^{\circ}$ hill. The skier is pulled a distance $x=220 \mathrm{m}$ along the incline and it takes 2.0 min to reach the top of the hill. If thecoefficient of kinetic friction between the snow and skis is $\mu_{k}=0.10,$ what horsepower engine is required if 30 such skiers $(\max )$ are on the rope at one time?

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26 $\mathrm{hp}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

McMaster University

Lectures

04:05

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.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

04:23

(II) A 65-kg skier grips a…

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04:44

A 63-kg skier grips a movi…

03:18

A 65-kg skier grips a movi…

03:11

A skier is pulled by a tow…

04:36

01:09

A skier of mass $70.0 \mat…

01:32

Rope Tow A skier is pulled…

02:44

A skier of mass $70 \mathr…

02:43

A skier of mass 70.0 $\mat…

02:38

A $50 \mathrm{~kg}$ skier …

01:35

Holding on to a towrope mo…

03:24

08:40

Sam, whose mass is $75 \ma…

03:35

by trying Let's start by drawing a free body diagram for this situation and we're gonna model Ah, the all 30 skiers as one as one body. Okay, so this is the one body. This is all three skiers and they have a gravitational force of mg on the hill here is inclined of angle fatal, which is 23 degrees. Then you have ah normal force. After Ben, you have ah pulling force after p and you have a course of fiction at sub f r and using a vector arrow to to, um to denote that they're all Metro's anywhere. This is a free body diagram in the situation. So what we do is we resolve forces um, first on DSO in the UAE direction, uh, you have normal force and forced to gravity. So normal force minus forced due to gravity which is mg signed. Leda Bart looks It would be n g ah co sign and you co sign Fada. Um is equal to zero. Right? So he was known Acceleration of the why direction So normal force is equal to m g co sign. They don't in the ex direction. You have to really forces you have absolute p exacting the positive extraction minus f cut. So that farce a force of friction minus the X component of gravity, which is mg signed data is equal to zero. So have superior is mg sine theta plus force affection, uh, lips for some affection. Remember, that force of fiction is, um, equal to music care, conversion of kinetic fiction times the normal force, and we just established where bat is. So this is music a times mg co sign data. Okay. Therefore, we have that, uh, important force and she signed Tate up, plus music care times mg, Cho San taito. And so this gives us if we take Angie common, we get MG time. Science data plus music. Kay turns co signed data. Okay, that's a setup. That's our force. Ah, and that is really the most are important. Ah, part of this problems. And the problem is finding the forests and florists, uh, is equal to, um from here. And she so m g would be for each skier has 75 kilograms of weight, 75 part mass, 75 kilograms times 9.8 meters per second squared. Multiply that by 30 because you're 30 skiers and then most play to that sign data. Plus, so sign 23. It is 23 plus Mrs Care, which is 230.1 Times Co signed 23. Okay. And this gives us 10,000 645 mutants, approximately four for the force. The pulling force that is exerted, that's a power now is equal to work down. Her average power has worked on you the time and so work done is force applied in a longer given distance over in the time and then that is divided over time. Um and so forest is 10,465 meetings distance. It's moved to 20 meters along the hill, and you divide that by two minutes, which is 120 seconds, giving you on average power of 19,500 and 16 once. And now we want this and horse powers horsepower. And so we recall that one horse power is equal to 746 watts. Multiply by one of the 7 46 and you get, uh, 26 horse powers for the average power, and that's it

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