# Understanding Work Done and the Role of Force in Solving Problems | 360J Example

• Nubcake
In summary, the confusion arises from the use of weight and force in the calculation of work done on an object. By convention, 0J potential energy is used at ground level, and when the barrel is raised 1.8m, it gains 360J of potential energy. The person pushing the barrel does positive work, while gravity does negative work. The net work done on the object is 0, explaining why it does not gain any kinetic energy.
Nubcake
I have always managed to solve problem asking how much work is being done but then once I start to think about the work being done I get confused. E.g A barrel of weight 200N is raised by a vertical distance of 1.8m by being moved along a ramp. The work done here would be 200 x 1.8 =360J . I do not understand why 200N is used since it is the weight acting vertically downwards opposite the distance moved in the direction of the force. So why is work being done shouldn't work be done when the barrel is moving in the same direction as its own weight? Or is it that 200N is the force that the person is giving to move it up along the ramp hence it is in the same direction of the force.Can someone clear this up for me?

When you change heights you change the barrel's potential energy. By convention we arbitrarily use 0J potential energy at ground level and when you raise it 1.8 m then you get PE = F * d = 200N * 1.8m = 360 J then if you let it fall back to the ground it have 360 J of kinetic energy of movement at ground level which it then dissipates on impact.

jedishrfu said:
When you change heights you change the barrel's potential energy. By convention we arbitrarily use 0J potential energy at ground level and when you raise it 1.8 m then you get PE = F * d = 200N * 1.8m = 360 J then if you let it fall back to the ground it have 360 J of kinetic energy of movement at ground level which it then dissipates on impact.

I was more concerned about the direction and the force ; doesn't the weight of the barrel act in the opposite direction of movement?

Nubcake said:
I was more concerned about the direction and the force ; doesn't the weight of the barrel act in the opposite direction of movement?

Yes. So the work done by gravity is negative (-360 J). By definition, the change in gravitational potential energy is equal to the negative of the work done by gravity. So, the change in potential energy is +360 J (potential energy increases when gravity does negative work).

The work done by the person pushing the thing up the ramp is positive, since the displacement and force are in the same direction. Let's assume that there is negligible friction. Let's also assume that the object is pushed up the ramp at a constant speed (neglecting the initial acceleration to get it moving). Then the forces parallel to the ramp have to be balanced, which means that the person pushes with a force equal to mgsinθ, which is the component of the weight that acts "down the ramp." The work done is then mgsinθ*d, where d is the distance traveled along the ramp. But from basic trigonometry, d = h/sinθ, so W = mgsinθ*(h/sinθ) = mgh.

The person does an amount of work equal to mgh = +360 J (but the ramp allows him to do so with a smaller force than if he just lifted it vertically).

Notice that the person does +360 J of work, and gravity does -360 J of work on the object, so the NET work done on the object is 0 (which makes sense because it has 0 net force on it). This explains why it does not gain any kinetic energy. (Recall that the work-energy theorem says that the work done on an object is equal to its change in kinetic energy).

What cepheid is saying is that he uses less force to push it up the ramp, but he has to push it for a greater distance. So the product of the force times the distance comes out the same as if he had just lifted it vertically with a larger force over a smaller distance.

## What is work and how is it calculated?

Work is the transfer of energy that results in an object being displaced. It is calculated by multiplying the force applied to an object by the distance it is moved in the direction of the force.

## What is the role of force in solving problems involving work?

Force is necessary for work to be done on an object. Without force, no energy would be transferred and no work would be done.

## How does the direction of force affect the work done on an object?

The direction of force is important in determining the work done on an object. If the force is applied in the same direction as the displacement, then all of the force contributes to the work done. However, if the force is applied in a different direction, only the component of the force in the direction of the displacement contributes to the work done.

## What are some real-life examples of work being done?

Some examples of work being done include lifting a book off a table, pushing a shopping cart, and pulling a wagon. Essentially, any time an object is being moved by a force, work is being done.

## How is the concept of work applied in different fields of science?

In physics, work is used to understand the transfer of energy and the motion of objects. In chemistry, work is used to understand chemical reactions and the formation of compounds. In biology, work is used to understand the movement and function of living organisms. In engineering, work is used to design and create machines and structures that can perform tasks efficiently.

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