Gravitional Potential Energy equation confusion.?

Question

Hi,

I'm revising for a Physics test and in my text book it says:

Using the formula W = fd we can say,

the change of its gravitational potential energy = its weight x its change in height.

This I understand. But... then it goes on to talk about GPE and mass.

and it tells me that,

the change in gravitational potential energy = mass x gravitational field strength x change in height

Now what I don't get is that they seem to be working out the same result but differently. Can someone please explain what they mean and why they're different?

Please and thank you!

Answer 1

They're the same thing.



GPE = wh

GPE = mgh



but w = mg



now do you see how they are the same thing?



You see if you multiply mass x gravitational field strength that gives you the weight.

Answer 2

By 'definition' (the work-energy theorem) GPE is gained from the external work that is done against gravitational force while raising a mass ..

That being the case .. using W = f x d, F is the weight of an object (mg Newtons**) and the distance change is a height raised/lowered (h metres)



So the work done against gravity (F x d) = mg.h which gives the formula for change in GPE (gain or loss depending on height increase or decrease)



(**Weight (N) = mass(kg) x grav field strength g (9.80 N/kg ≡ 9.80 m/s²)

GPE = gravitational PE

Answer 3

Potential Energy=PE

PE=F x d

PE is always measured with respect to a reference position,at which PE is taken zero by definition.Here we take ground as the reference position.Now we take a height h above it.So work done to bring the object to a height h is mg x h,since force on a object in a gravitational field is mg always.(from newton's second law force = mass x accn.)So work done to bring the object from a reference position to h=PE=mgh.

The 2 things you said are equivalent.GPE=weight xchange in height.weight=force on object=mg.So this is equivalent to PE=mgh which is same as we found out above by PE=Fxd.

Answer 4

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