Question

calculate the amount of work done in carrying a box on an inclined plane​

Answer 1

Answer:

Suppose an object is pushed up a smooth inclined plane from ground level to a point h above the ground with force F. The angle of inclination is A. How much work is done?

To push an object up a smooth inclined plane, one must overcome the force of gravity which causes the object to slide down the plane. Hence, the force F=mgsinA must be applied. We can denote the distance the body undergoes as s=hsinA, then:

W=Fs=mg(sinA)^2

The answer is mgh and I know that this can be easily proven using energy conservation laws, but I want to know why my method is incorrect.

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Jun 4 '15 at 10:49

Kas

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You've made a mistake in calculating the displacement component for the object. If you observe, S≠hsinAS≠hsinA

S=hsinA

S=hsin⁡A

and therefore, the work done, is:

F.s=(mgsinA)(hsinA)=mgh

F.s=(mgsin⁡A)(hsin⁡A)=mgh

which is the exact expression you got from energy conservation.

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Jun 4 '15 at 11:12

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Work done on a object by definition is W=F⋅SW=F⋅S. This is a vector product so you can project one vector on the another to get the result. At first you were projecting the force FF on the displacement SS. You got the answer here and projecting the displacement on the vertical axis and multiply it by the force along the slope is meaningless.

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