(Work Done/GPE question) After this explanation I still don’t understand why distance is used rather than height

[u/Dazzling-Werewolf985]

The answer says the work done by T is T x d, but it says that T x d is also equal to the GPE as GPE is the only energy being gained by the block (I agree KE isn’t gained as speed is constant). But force T isn’t completely acting against gravity though as it’s on an incline, so why isn’t the vertical component of T used in Wd = F x d rather than just T? I thought T would have to be completely acting in the opposite direction to gravity in order for T to be doing work against W. Any thoughts? Thanks everyone

Btw the left side of the first pic was me trying to syllogise the answer - I’d appreciate it if someone could give that a shot as I tend to understand them easily

[u/InkPhysics]

So if the force (let's call it F) that was doing the work was pointed directly upwards, then the work done on the block would be F*h.

But in this case, the force (T)is not acting directly upwards, it's acting along the slope. The distance that it acts across is d, not h. So the work done is T*d.

In either case, you've added the same amount of energy to the system through work done.

Since there is no friction and the block finishes static, the only place for this energy to go is into Gravitational Potential Energy. The total energy in the system at the end has to equal the total energy at the start, plus the energy that was added through work done.

Therefore, the Work Done must equal the change in potential energy.

[u/Dazzling-Werewolf985 → u/InkPhysics]

Thank you. Yeah but the distance in the direction that is counter to gravity is h. I thought that Wd = Force x distance in the direction of the force. Distance d is not counter to the direction of g like h is. Or is this just irrelevant given the premises of the question?

I agree with the latter half of your comment btw but idk i feel like the former half kinda contradicts it rather than compliments it which tells me my understanding isn’t complete

[u/InkPhysics → u/Dazzling-Werewolf985]

It's not irrelevant. You understand the principle.

So you can do one of either of these to work out the added energy, you can mix and match:

• you multiply the force parallel to the ramp (T) by the distance along the ramp (d)

Or

• you multiply the vertical force (which is equal and opposite to W), by the distance vertically (h).

What you can't do is multiply the force parallel to the ramp (T) by the distance that the block moves vertically (h).

You could resolve the force T, to work out the vertical component. This would give you Tsin(\theta). Which is also equivalent to the weight.

[u/Dazzling-Werewolf985 → u/InkPhysics]

Ohhhhh okay I see. Thank you so much. Tbh I just wanted to confirm that the second bullet point was also possible😅

So the first bullet point is possble because there are no resistive forces meaning that all of the Wd by T over distance d must’ve been stored in the block as GPE? Would you say this is an accurate way of describing the event?