Cycling Up a Hill: Calculating Work Against Gravity

[zaddyzad]

Homework Statement

(III) A cyclist intends to cycle up a 7.50° hill whose vertical
height is 125 m. The pedals turn in a circle of diameter
36.0 cm. Assuming the mass of bicycle plus person is
75.0 kg, (a) calculate how much work must be done against
gravity.

The Attempt at a Solution

My question is about the wording about a. Work done against gravity is done by the cyclist right? So Shouldn't the computation of this be W = mgh + W(done by sliding force) and not just mgh?

Can explain the wording of these type questions. The way it seems to me it's asking the work done by the cyclist.

 

[haruspex]

What sliding force?

 

[CWatters]

There is no mention of friction (sliding force?) in the problem.

 

[zaddyzad]

By sliding force I mean the component of gravity opposing motion.

 

[zaddyzad]

So I'm thinking mgh = Work done by cyclist - Work done by gravity, and when it asks work done against gravity I'm assuming its asking for the work done by the cyclist.

I need wording clarification.

 

[haruspex]

By sliding force I mean the component of gravity opposing motion.

Gravity does not oppose motion.

 

[zaddyzad]

But gravity is doing work against the cyclist no... ? Its pulling him backwards as he tries cycling upwards.

 

[CWatters]

Not backwards, downwards. The work done against gravity is mgh.

Look at it this way... The PE gained climbing a mountain is mgh right? Note that mgh does not say anything about the route taken. It does not make a difference if you take the longer but easier route or the shorter steeper route (ignoring the fact that humans might be more efficient taking one route or the other)

 

[haruspex]

Not backwards, downwards. The work done against gravity is mgh.

Look at it this way... The PE gained climbing a mountain is mgh right? Note that mgh does not say anything about the route taken. It does not make a difference if you take the longer but easier route or the shorter steeper route (ignoring the fact that humans might be more efficient taking one route or the other)

... and the work gravity is 'doing' against the cyclist is negative. The force of gravity is downwards but the cyclist's displacement is upwards, so the two have opposite sign, and thus a negative product.