Work done by gravity and the minus sign

AI Thread Summary
The discussion centers on the concept of work done by gravity when a person climbs, questioning why the work is considered positive despite gravity acting downward. It clarifies that while gravity does negative work on the climber, the climber's exertion results in positive work as they gain potential energy. The conversation emphasizes that the lifting force does positive work while gravity does negative work, and the power output reflects the rate of energy transfer from the climber's muscles to the potential energy of the body. The work-energy theorem is referenced, highlighting that the work done by the net force must equal zero when the object is raised at constant speed. Overall, the distinction between the forces at play and their respective contributions to work is crucial for understanding this scenario.
Mohmmad Maaitah
Messages
90
Reaction score
20
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
 
Physics news on Phys.org
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.
 
  • Like
Likes MatinSAR, jbriggs444 and malawi_glenn
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).
 
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.
 
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."
 
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.
 
  • Like
Likes MatinSAR, paulimerci, Lnewqban and 1 other person
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)}##.
 
  • Like
Likes MatinSAR and Lnewqban
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.
 
  • Like
Likes MatinSAR, berkeman and kuruman
Back
Top