Understanding Work Components in Calculating Net Work Done

[Dylan R]

Homework Statement

Homework Equations

The Attempt at a Solution

I do not understand why is mgh2 is being subtracted from the overall equation instead of added.
I am able to construct each of the work components but when building the overall equation I'm having a problem of understanding when is each component should be added or subtracted (except for the friction which make sense to subtract) [/B]

 

[haruspex]

why is mgh2 being subtracted

The positive terms are those which add to the KE of the block. Will coasting uphill increase it or reduce it?

 

[Dylan R]

The positive terms are those which add to the KE of the block. Will coasting uphill increase it or reduce it?

Reduce
So basically it is the KE that is equal to mgh2 (closed system) that is being subtracted ?

 

[haruspex]

Reduce

So what sign should it have?

 

[Dylan R]

So what sign should it have?

-
So basically we treat it as a closed system by saying that mgh2=KE that is being subtracted ?

 

[haruspex]

-
So basically we treat it as a closed system by saying that mgh2=KE that is being subtracted ?

Treating what as a closed system? The block is certainly not a closed system by itself. It is acted on by external forces and these change its KE. But we know it starts and ends at rest, so the net work done on it is zero. Going down the slope, gravity does positive work on it, but going up the slope gravity does negative work on it.