Physics energy transfer on slope

splitter2017

here is a basic question: Which uses more energy, to lift a mass,m, vertically upwards to height h OR to pull it up (to the same height, h) along a SMOOTH inclined plane.

Now using equations it shows the energy required is the same for both scenarios:
Lifting directly up:
Work done = mgh

Pulling up a slope:
Work done = F * d where d is distance along the plane (the hypotenuse of the triangle)

Therefore, Work done = mgsin( ϴ) * d
= mgsin( ϴ) * h/sin( ϴ)
given that sin( ϴ) = opposite/hypotenuse
so this cancels to Work done = mgh

This proves the energy transferred (work done is the same for both). However, surely work is done in the horizontal direction too. How on earth can it require the same amount of energy to move an object upward a height h and also along a horizontal distance x (imagine if the horizontal distance were really really big) as it would just lifting it up to height h. The actually theoretical reasoning is confusing me.

(edited 6 years ago)

Reply 1

splitter2017

Would the work done for the slope scenario be...
Work done = mgh + F*dcos(ϴ) whatever the angle and force happened to be

Reply 2

RogerOxon

Original post by splitter2017

This proves the energy transferred (work done is the same for both). However, surely work is done in the horizontal direction too. How on earth can it require the same amount of energy to move an object upward a height h and also along a horizontal distance x (imagine if the horizontal distance were really really big) as it would just lifting it up to height h. The actually theoretical reasoning is confusing me.

GPE is only a function of height.

The inclined plane is smooth, so moving the block horizontally required no force / work. Practical inclined planes would.

(edited 6 years ago)

Reply 3

splitter2017

Original post by RogerOxon

There'

GPE is only a function of height.

The inclined plane is smooth, so moving the block horizontally required no force / work. Practical inclined planes would.

so does this mean If I pushed an object along a perfectly horizontal surface (no friction) a distance d then it requires no energy?

Reply 4

RogerOxon

Original post by splitter2017

so does this mean If I pushed an object along a perfectly horizontal surface (no friction) a distance d then it requires no energy?

Yes.

Work done is scalar product of force and distance. To move an object with no resistance requires no force.

Reply 5

splitter2017

Original post by RogerOxon

Yes.

Work done is scalar product of force and distance. To move an object with no resistance requires no force.

ok but surely if it was accelerating (F (resultant) = ma ) and there is then a force acting to cause the rate in change of momentum and hence work is being done?

Reply 6

RogerOxon

Original post by splitter2017

ok but surely if it was accelerating (F (resultant) = ma ) and there is then a force acting to cause the rate in change of momentum and hence work is being done?

Any work done to accelerate the mass will be returned when it is stopped. The net work done is therefore zero.

The force will do work to impart kinetic energy to the mass, but that energy will be returned by the force doing negative work to stop the mass.