# Work-Energy in carrying something down

• lightlightsup
In summary: If I were to pull an object up towards the Earth and decrease its K, I'm subtracting from the Wg (mgdcos0) (work being done by gravity to decrease the object's K).
lightlightsup
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.

lightlightsup said:
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
PeroK said:
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
lightlightsup said:
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

lightlightsup said:
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 said:
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.

PeroK said:
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.

PeroK
@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).

## What is work-energy?

Work-energy is a concept in physics that refers to the relationship between the work done on an object and the change in its kinetic energy. It is used to describe the transfer of energy that occurs when an object is moved by a force.

## How does work-energy relate to carrying something down?

When carrying something down, you are exerting a force on the object to move it against the force of gravity. This work done on the object is then converted into the kinetic energy of the object as it moves downward. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.

## What factors affect the work-energy involved in carrying something down?

The amount of work-energy involved in carrying something down depends on the mass of the object, the distance it is carried, and the force exerted to move it. The steeper the incline or the heavier the object, the more work is required to move it downward.

## How is work-energy calculated when carrying something down?

The work-energy involved in carrying something down is calculated by multiplying the force exerted on the object by the distance it is carried. This is equal to the change in kinetic energy of the object.

## What are some real-life applications of work-energy when carrying something down?

Work-energy is a fundamental concept in physics and is applicable in various real-life situations. For example, when carrying groceries down a flight of stairs, work-energy is involved in moving the bags against the force of gravity. Similarly, when a person walks down a hill, work-energy is involved in moving their body against the force of gravity.

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