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A physics professor is pushed up a ramp inclined upward at an angle theta above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is m. He is pushed a distance x along the incline by a group of students who together exert a constant horizontal force of F. The professor's speed at the bottom of the ramp is v.

Use the work-energy theorem to find his speed at the top of the ramp.

I know W=K2-K1 and K=.5mv'2 but i dont understand

would it be K= .5mv'2 sin(theta)

I also know F=-kx but how would i equate that for this problem/

please help!

2007-11-13 19:04:51 · 2 answers · asked by Anonymous in Science & Mathematics Physics

2 answers

Your question is inconsistent. You are pushing the mass m up the ramp, but you give a speed v at the bottom of the ramp. Here's what I think you meant.

You push the prof and chair m up the ramp inclined at theta a distance s along the ramp's surface using a force F along the surface. What would be the velocity of the prof and chair at the bottom of the ramp if both are let go and they slide back down. If that's what you meant, here's the answer.

WE = mgh = mg s sin(theta); where m is the prof and chair mass, g = 9.81 m/sec^2 on Earth's surface, s = the distance pushed up the ramp, theta is the incline, and h is the vertical height of the mass m above a ground level (h = 0). WE is the work energy expended using the so-called work function.

As WE = mgh = PE, we see the amount of work put into the mass equals the potential energy of the mass at height h. In other words, the work is what gave the prof and chair potential energy.

Now the second part, what's v at the bottom of the ramp after letting the prof and chair slide down from h? We invoke the conservation of energy. Thus, PE = mgh = mg s sin(theta) = 1/2 mv^2 = KE, which simply says that all the PE at h is converted into kinetic energy at h = 0...the bottom of the ramp. In which case g s sin(theta) = v^2/2 so that v^2 = 2gs sin(theta) or v = sqrt(2gs sin(theta)).

And there you have it. The work put into the mass of the prof and chair is where the potential energy came from. And the velocity at the bottom of the ramp came from converting the potential energy into kinetic energy.

BTW...as you assumed frictionless rollers, F = - kx, the friction equation, has no bearing on the problem. That is, no work is expended against friction because there is no friction by your assumption.

2007-11-13 20:19:58 · answer #1 · answered by oldprof 7 · 0 0

actually, gravity IS a force. Anything that has mass, has gravity. Yes, blackholes suck light. Light has no mass because nothing with mass can achieve light speed. Light does not work the same way as other things in the universe because light and time are warped by mass. If there was nothing in space, yes, gravity would still exist. Think of gravity like a blanket stretched tightly through the universe. When a planet is placed on the sheet, the sheet bends in a hole around the mass. If there was no mass, the "sheet" would still be there, just no hole.

2016-05-23 02:41:27 · answer #2 · answered by dorothy 3 · 0 0

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