# Work and Energy on a Slope - How Does a Block Move Up with Zero Net Work?

• JackyCheukKi
In summary, the conversation discusses the concept of work and energy in relation to a block being pulled up a slope with a string. According to the network theorem, the net work is equal to the change in kinetic energy, but the problem arises when the net work is zero and the block still moves up the slope. The solution to this dilemma is that while the block gains potential energy, it does not gain kinetic energy due to the net work being zero. This is because the work of the tension in the string is equal to the negative work of the weight, resulting in a gain of potential energy for the block.
JackyCheukKi
Homework Statement
Relevant Equations
energy initial(of one object) + net work done on the object = energy final??
Guys, I have a problem that really needs you guys to help, I know it is a stupid question but please bear with me:

Context:
You have a block on a slope(has friction) you use a string to pull the block up with constant speed.

Problem:
So according to the network theorem, the work net is equal to the change in kinetic energy, and here we can see that the kinetic energy remains the same and the net work should be zero. But my problem is if the net work is zero, how the heck did the block move up the slope?? if it moves up the slope, it gains POTENTIAL ENERGY right??

isn't Energy(initial) + net work = Energy(final) ?

Delta2
One must be careful not to count the effects of gravity twice. Either you include the work done by gravity as a force or the change in gravitational potential energy, but not both. (Gravitational PE already includes work done by gravity.)

There are several ways to look at the Work-KE theorem. If you include the work done by ALL forces, including gravity, then no net work is done on the block as it is pulled up the incline. Thus the KE doesn't change. So what? While there's no net work done, whoever is pulling the string is certainly doing work!

On the other hand, you can also view it in terms of energy: Initial energy + work done = final energy. If your energy term includes gravitational PE, then the "work done" means the work done by all forces except gravity. That "work done" will not be zero, since PE increases.

Delta2, Lnewqban, Steve4Physics and 2 others
I have a slightly different view from @Doc Al's.

By definition, the net work done on a rigid body is the work done by the net force. Thus, it is equal to the gain in KE. Always. The gain in PE is not considered work done on the body; rather it is work done on the system consisting of the two gravitationally attracted bodies.

You are confusing net work done on the body with the work done by just one applied force, the tension in the string. While the speed is constant, ignoring friction, that is equal and opposite to the work done by gravity.

The precise wording in post #1 suggests the body starts at rest, so you do have to do some net work on it to get it going, though this can be arbitrarily small, depending how much of a hurry you are in. If it also finishes at rest, and there's no friction, you will stop pulling a little before that.

Delta2
Yes the block gains potential energy but doesn't gain kinetic energy because the net work is zero. Because the net work is zero the work of the tension equals minus the work of the weight. As you probably know the gain in potential energy equals also minus the work of the weight, hence it is equal to the work of the tension. To summarize it:
• Gain in kinetic energy=net work=0
• Gain in potential energy=-work of weight=work of tension

Last edited:

## What is the work-energy theorem?

The work-energy theorem is a fundamental concept in physics that states that the work done on an object is equal to the change in its kinetic energy. In other words, the amount of energy transferred to or from an object is equal to the difference in its initial and final kinetic energy.

## How is the work-energy theorem calculated?

The work-energy theorem is calculated by multiplying the force applied to an object by the distance it moves in the direction of the force. This can be represented by the equation W = Fd, where W is work, F is force, and d is distance. Alternatively, it can also be calculated by taking the difference between an object's initial and final kinetic energy.

## What is the significance of the work-energy theorem?

The work-energy theorem is significant because it allows us to understand the relationship between work and energy. It also helps us to analyze and predict the motion of objects by considering the forces acting on them and the resulting changes in their kinetic energy.

## Can the work-energy theorem be applied to all types of motion?

Yes, the work-energy theorem can be applied to all types of motion, including linear, rotational, and oscillatory motion. It is a universal principle that applies to all objects and systems in motion.

## Are there any limitations to the work-energy theorem?

While the work-energy theorem is a useful and accurate concept, it does have some limitations. It assumes that there are no external forces acting on the object besides those being considered, and it does not take into account factors such as friction or air resistance. Additionally, it only applies to conservative forces, which do not dissipate energy as heat.

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