Work-Energy in carrying something down

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Homework Statement

Sara carries a heavy box of books down a flight of stairs from the third floor to the first floor. Which one of the following statements best describes the work done on the box by Sara?

Relevant Equations

Wa=-Wg

Options are:

a) Sara doesn’t do any work on the heavy box of books.
b) Sara does a small amount of negative work on the heavy box of books.
c) Sara does a small amount of positive work on the heavy box of books.
d) Sara does a large amount of negative work on the heavy box of books.
e) Sara does a large amount of positive work on the heavy box of books.

Apparently, the answer is: "d) Sara does a large amount of negative work on the heavy box of books."

Can someone please explain why to me?
I'd like more than a definition-like answer so I can better understand the Work-Energy concepts here.

 

[PeroK]

Homework Statement: Sara carries a heavy box of books down a flight of stairs from the third floor to the first floor. Which one of the following statements best describes the work done on the box by Sara?
Homework Equations: Wa=-Wg

Options are:

a) Sara doesn’t do any work on the heavy box of books.
b) Sara does a small amount of negative work on the heavy box of books.
c) Sara does a small amount of positive work on the heavy box of books.
d) Sara does a large amount of negative work on the heavy box of books.
e) Sara does a large amount of positive work on the heavy box of books.

Apparently, the answer is: "d) Sara does a large amount of negative work on the heavy box of books."

Can someone please explain why to me?
I'd like more than a definition-like answer so I can better understand the Work-Energy concepts here.

Do the books lose or gain energy in the process of being carried downstairs?

 

[lightlightsup]

Do the books lose or gain energy in the process of being carried downstairs?

They lose potential energy.
So, there is negative work being done on the books because the books are losing gravitational potential energy?

 

[PeroK]

They lose potential energy.
So, there is negative work being done on the books because the books are losing gravitational potential energy?

Yes. Another way to think about it is what would have happened to the books if Sara wasn't carrying them? Assume nothing else got in the way!

 

[lightlightsup]

Does this also make sense as an explanation?
Books carried down:
ΔK = Kf - K0 = Wa + Wg
0 = Wa + Wg
Wa = -Wg
Wg = mgd cos φ
φ = 0°
∴ Wa = -mgd

So, if the books were being carried up:
ΔK = Kf - K0 = Wa + Wg
0 = Wa + Wg
Wa = -Wg
Wg = mgd cos φ
φ = 180°
∴ Wa = -(-mgd) = mgd

 

[PeroK]

Does this also make sense as an explanation?
ΔK = Kf - K0 = Wa + Wg
0 = Wa + Wg
Wa = -Wg
Wg = mgd cos φ
φ = 180°
∴ Wa = -mgd

You'll need to explain what all those steps mean.

 

[lightlightsup]

Does this also make sense as an explanation?
Books carried down:
ΔK = Kf - K0 = Wa + Wg
0 = Wa + Wg
Wa = -Wg
Wg = mgd cos φ
φ = 0°
∴ Wa = -mgd

So, if the books were being carried up:
ΔK = Kf - K0 = Wa + Wg
0 = Wa + Wg
Wa = -Wg
Wg = mgd cos φ
φ = 180°
∴ Wa = -(-mgd) = mgd

The ΔK of the books here is 0.
But, there is displacement (d), so there is only work being done by Sara (Wa, work applied) and work being done by gravity (Wg). Their sum must be 0 whether the books are being moved up or down.
If the displacement is down, the angle between Fg (mg) and d is 0°, and cos 0° = 1.
If the displacement is up, the angle between Fg (mg) and d is 180°, and cos 180° = -1.
Your initial explanation is much better and more intuitive but I haven't gotten to really studying U (potential energy) yet.

 

[lightlightsup]

Yes. Another way to think about it is what would have happened to the books if Sara wasn't carrying them? Assume nothing else got in the way!

The books would gain kinetic energy and lose potential energy.
Therefore, Sara did negative work to prevent the books from gaining kinetic energy.
She "took energy from the object (books)", therefore it is -W.

 

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@PeroK : Thank You.
ΔK = Kf - K0 = Wa + Wg
This equation also makes a lot more sense now.
If I were to push an object down towards the Earth and increase its K, I'm adding to the Wg (mgdcos0) (work being done by gravity to increase the object's K).