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A person is pushed up a ramp inclined upward at an angle θ above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the person 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 FA. The person’s speed at the bottom of the ramp is v0 m/s. Use the work-energy theorem to find his speed at the top of the ramp.

Respuesta :

gcosarinsky

Hi!

The work W done by force FA is W = FA*cos(θ)

The work-energy theorem say that the work W done by nonconservative forces is equal to the variation of mechanical energy:

[tex]W = \Delta E_{potential} + \Delta E_{kinetic}[/tex]

If the distance moved is x, then the vertical displacement is x*sin(θ) Then,

[tex]\Delta E_{potential} = mgx \sin(\theta)[/tex]

[tex]\Delta E_{kinetic} = \frac{m}{2}v^2 =  W - \Delta E_{potential} = FA\cos(\theta) - mgx\sin(\theta)[/tex]

We can solve for the speed v at the top of the ramp:

[tex]v = sqrt (\frac{2}{m} ( FA\cos(\theta) - mgx\sin(\theta)))[/tex]

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