Work done by gravity and the minus sign

In summary, the problem is about the rate at which mechanical energy is transferred from the muscles to the altitude (potential energy) of the body. The body gains potential energy and the calculated power reflects how quickly that energy is gained and stored. The lifting force provided by the Marine does positive work while gravity does negative work. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Therefore, the raising force does positive work on the object. The work done by gravity on the object is the negative of the work done by the raising force, and is equal to the change in gravitational potential energy.
  • #1
Mohmmad Maaitah
87
19
Homework Statement
As in picture
Relevant Equations
Work by gravity = -mgh
Shouldn't work be minus when the man climbing up and force on him is down?
shouldn't the power be also in minus?
Can someone explain to me why is it positive please!
WhatsApp Image 2023-05-02 at 13.36.58.jpg


WhatsApp Image 2023-05-02 at 13.36.59.jpg
 
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  • #2
Mohmmad Maaitah said:
Homework Statement: As in picture
Relevant Equations: Work by gravity = -mgh

Shouldn't work be minus when the man climbing up and force on him is down?
shouldn't the power be also in minus?
Can someone explain to me why is it positive please!
Because it asks for the man's power output, i.e. the rate at which the man does work against gravity. You have calculated the rate at which gravity does work on the man.
 
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  • #3
Mechanical energy can only be transferred from one body to another.
The problem is about the rate at which mechanical energy is transferred from the muscles to the altitude (potential energy) of the body.
From that point of view, the body has gained potential energy (hence, positive work).
The calculated power reflects how quickly that energy has been gained and stored.

Once stored in form of potential energy, it could be transferred to another body.
For example, the man drops down to ground level while a rope around a pulley lifts certain weight up to the altitude he was at.
In that case, the body loses energy (hence, negative work).

On the other hand, the lifted weight has gained potential energy (it has received work or energy; therefore, positive work).
 
  • #4
Lnewqban said:
Mechanical energy can only be transferred from one body to another.
The problem is about the rate at which mechanical energy is transferred from the muscles to the altitude (potential energy) of the body.
From that point of view, the body has gained potential energy (hence, positive work).
The calculated power reflects how quickly that energy has been gained and stored.

Once stored in form of potential energy, it could be transferred to another body.
For example, the man drops down to ground level while a rope around a pulley lifts certain weight up to the altitude he was at.
In that case, the body loses energy (hence, negative work).

On the other hand, the lifted weight has gained potential energy (it has received work or energy; therefore, positive work).
The terms positive and negative preceding "work" are meaningless if you do not specify the force that does the work. When the body is lifted you say that the body has gained potential energy (correct) and you conclude "hence positive work." That's debatable. There is no default force that does work. The correct conclusion is "hence the lifting force does positive work and gravity does negative work." In this case the lifting force is provided by the Marine. The Marine's power output is positive at the expense of biochemical power generated in the Marine's muscles.
 
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  • #5
kuruman said:
The terms positive and negative preceding "work" are meaningless if you do not specify the force that does the work. When the body is lifted you say that the body has gained potential energy (correct) and you conclude "hence positive work." That's debatable. There is no default force that does work. The correct conclusion is "hence the lifting force does positive work and gravity does negative work." In this case the lifting force is provided by the Marine. The Marine's power output is positive at the expense of biochemical power generated in the Marine's muscles.
I appreciate your observation, @kuruman

This part is not clear to me:
The correct conclusion is "... and gravity does negative work."
 
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  • #6
Lnewqban said:
I appreciate your observation, @kuruman

This part is not clear to me:
The correct conclusion is "... and gravity does negative work."
When an object is raised the vertical displacement vector ##\vec d## forms an angle of 180° with the force of gravity ##\vec F=m\vec g##. The work done by gravity on the raised object is $$W_g=\vec F\cdot \vec d=Fd\cos(180^{\circ})=Fd(-1)<0.$$ If the object is raised at constant speed, its kinetic energy does not change. By the work-energy theorem the work done by the net force must be zero, therefore the work done by the raising force is the negative of the work done by gravity, i.e. the raising force does positive work on the object.
 
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  • #7
It may also be worth mentioning the role of gravitational potential energy (GPE).

Being a conservative force, gravity has its own ‘energy store’, i.e. GPE.

When gravity does positive work (e.g. accelerating a free-falling stone) the work done by gravity (positive) is the decrease in GPE. Stored GPE is 'used up'.

When gravity does negative work (e.g. when we climb a ladder) the work done by gravity (negative) is the increase in GPE. We increase the stored GPE.

##\text {Work done by gravity} = -\Delta \text {(GPE)}##.
 
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  • #8
kuruman said:
By the work-energy theorem the work done by the net force must be zero, therefore the work done by the raising force is the negative of the work done by gravity, i.e. the raising force does positive work on the object.
Clear now, professor.
Again, thank you.
 
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