Net force = 0, but potential increases?

[SprucerMoose]

G'day,

Just wondering if someone can explain to me how when an object is moved to a higher point above the earth, if initial velocity = final velocity, the net work done is zero? The way I see it the object now has a greater gravitational poitential energy and although no kinetic energy is gained, it has gained potential energy.

Any help would be appreciated.


Thanks

 

[rcgldr]

You question differs from the title. If there's no net force, it just means that an object is traveling at constant velocity. In the case of gravity, then there is a second force that is opposing gravity in order for the net force to be zero. A simple case would be an object falling a terminal velocity where aerodynamic drag is equal and opposite to gravity.

If you only consider the two equal and opposing forces involved, then no work is done, even though the object is moving with constant velocity and may experience a change in potential energy with respect to one of those forces, such as gravity. You'd need to factor in the energy input associated with the force opposing gravity to account for the change in potential energy. For example, a pump could be pressurizing a cylinder, causing a piston to rise at constant speed, and assuming zero losses, the energy consumed by the pump would equal the gravitational potential energy gained by the piston.

 

[I like Serena]

G'day,

Just wondering if someone can explain to me how when an object is moved to a higher point above the earth, if initial velocity = final velocity, the net work done is zero? The way I see it the object now has a greater gravitational poitential energy and although no kinetic energy is gained, it has gained potential energy.

Any help would be appreciated.


Thanks

Your intuition is correct.
In other words the net work done is not zero.

-- I like ILSe

 

[Doc Al]

Your intuition is correct.
In other words the net work done is not zero.

No, the net work done--including all forces--is zero. That's why the kinetic energy remains constant. Since gravity is continually doing (negative) work on the object as it is raised, work must also be done by some other force (your hand, perhaps) to lift the object at constant speed.

When you consider gravitational potential energy you are using that to represent the force of gravity. You then only consider the work done by other forces. In that case, work must be done to raise the object (by some external force) since the potential energy increases.

Note that either way you get the same answer. It's just very convenient to represent conservative forces such as gravity by potential energy terms.

 

[SprucerMoose]

So if the work done by gravity is increasing the potential energy, what is the work done by the lifter doing?

 

[Doc Al]

So if the work done by gravity is increasing the potential energy, what is the work done by the lifter doing?

No, the work done by the lifter is increasing the potential energy.

 

[I like Serena]

So if the work done by gravity is increasing the potential energy, what is the work done by the lifter doing?

Actually your hand does work on the object, resulting in a higher potential energy of the object.
Gravity pushes against your hand, doing work on your hand, making you lose some kind of energy.

 

[Dale]

Hi SprucerMoose,

When doing problems of this kind it is important to clearly define exactly what your "system" boundaries are. For compatibility with previous responses, let's say that the lifter is a human. If your system is the human then net work is done by the human on the object, raising its GPE. On the other hand, if your system is the human+object+earth then no net work is done on the system as all of the forces are internal.

In either case the net force is 0 and you have a transfer of energy from chemical potential energy in the human to gravitational potential energy of the object. Whether or not that is considered net work depends on your arbitrary choice of system boundaries.

 

[SprucerMoose]

I am beginning to make sense of this.

But back to the earlier pump example. If the pressurised liquid or gas is doing work on the piston to increase the potential energy, what work would the gravity be doing?

 

[Rap]

I am beginning to make sense of this.

But back to the earlier pump example. If the pressurised liquid or gas is doing work on the piston to increase the potential energy, what work would the gravity be doing?

The work done by gravity is the force of gravity times the distance moved. Since the force and the distance moved are in opposite directions, the work done on the system by gravity is negative. Add the work done by gravity to the work done by the pump, and you get zero.

 

[rcgldr]

But back to the earlier pump example. If the pressurised liquid or gas is doing work on the piston to increase the potential energy, what work would the gravity be doing?

Equal and opposing work. The work done on the piston cancels (no change in kinetic energy). The work consumed by the pump (it needs an energy source to operate) will equal the increase in gravitational potiential energy. What I did with the pump example is to take a larger view of the process to include the energy associated with the force opposing gravity.