# What is the Work Done by a Force Moving an Object from the Origin to x=5.0m?

• dareupgang
In summary, The conversation is discussing a homework problem involving a force and an object's movement. The work done by the force is represented by the equation W= ∫Fx dr, and the solution involves evaluating the integral and possibly factoring out a constant.
dareupgang

## Homework Statement

A force F = (4xi + 3yj) N acts on an object as the object moves in the x direction from the origin to x = 5.0m. Find the work W= Integral F x dr done by the force on the object

W= ∫Fx dr

## The Attempt at a Solution

∫4xi 2x^2 0 to 5

I checked the solution manual and for some reason they extracted the 4 outside the integral 4 ∫(x^2)/2 0 to 5

Is the 4 a constant ? is that why they pulled it out

dareupgang said:
I checked the solution manual and for some reason they extracted the 4 outside the integral 4 ∫(x^2)/2 0 to 5

Is the 4 a constant ? is that why they pulled it out

Probably a typo.

4 is just a number, how can it not be a constant?

## 1. What is the meaning of "W = Integral force" in science?

In science, the equation "W = Integral force" represents the relationship between work and force. It states that the amount of work done on an object is equal to the integral of the force applied to the object over a given distance.

## 2. How is the equation "W = Integral force" used in scientific experiments?

The equation "W = Integral force" is used in scientific experiments to calculate the work done on an object by a force. This allows scientists to understand the energy transfer and transformations that occur in a system.

## 3. What are some real-life examples of "W = Integral force"?

Some real-life examples of "W = Integral force" include lifting an object against gravity, pushing a cart up a hill, or pulling a sled across the snow. In all of these scenarios, work is being done on the object by a force.

## 4. How does the direction of force affect the value of "W = Integral force"?

The direction of force does not affect the value of "W = Integral force" as long as the force remains constant. This is because the integral of a constant function is equal to the product of the function and the distance over which it is applied.

## 5. Can "W = Integral force" be used for non-constant forces?

Yes, "W = Integral force" can be used for non-constant forces. In this case, the integral must be evaluated using calculus techniques, such as integration by parts or substitution, to determine the total work done on the object by the varying force.

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