# Finding Work from Force Equation

• mintsnapple
In summary, when solving a problem involving a changing force, you need to integrate the force with respect to x and use the positions as your limits.
mintsnapple

W = F*d

## The Attempt at a Solution

a. W = Ce^(ax)*2a^-1
b. W = Ce^(ax)*2a^-1
c. w = Ce^(ax)*(-4a^-1)

I feel like this problem is more than just this simple...

mintsnapple said:

W = F*d

## The Attempt at a Solution

a. W = Ce^(ax)*2a^-1
b. W = Ce^(ax)*2a^-1
c. w = Ce^(ax)*(-4a^-1)

I feel like this problem is more than just this simple...
Those results don't look right.

What do you get for the indefinite integral ## \displaystyle \int C e^{\alpha x}\ dx \ \ ? ##

1 person
SammyS said:
Those results don't look right.
... in particular, there should not be any x in the answers.

1 person
Ah, I just re-read the question and saw my mistake.

How would I approach this problem with a changing force though? Do I just plug in the end position, and multiply that force by displacement?

mintsnapple said:
Ah, I just re-read the question and saw my mistake.

How would I approach this problem with a changing force though? Do I just plug in the end position, and multiply that force by displacement?
dW = F dx .

You need to integrate to integrate the force with respect to x .

1 person
SammyS said:
dW = F dx .

You need to integrate to integrate the force with respect to x .

Ahh, I see. So integrate the force with respect to x, and use the positions as my limits.

mintsnapple said:
Ahh, I see. So integrate the force with respect to x, and use the positions as my limits.

Yes.

## 1. How do you calculate work from force equation?

The formula for calculating work from force equation is W = F * d, where W represents work, F represents force, and d represents displacement.

## 2. What units are used for force and displacement in the work equation?

Force is typically measured in Newtons (N) and displacement is measured in meters (m) in the work equation. However, other units such as joules (J) and centimeters (cm) can also be used depending on the system of measurement being used.

## 3. Can the work equation be used for both constant and non-constant forces?

Yes, the work equation can be used for both constant and non-constant forces. However, in the case of non-constant forces, the work done is equal to the area under the force-displacement curve.

## 4. How is the direction of work determined in the work equation?

The direction of work is determined by the direction of the applied force and the direction of the displacement. If the force and displacement are in the same direction, then the work is considered positive. If they are in opposite directions, then the work is considered negative.

## 5. What are some real-life applications of the work equation?

The work equation has many real-life applications, including calculating the energy needed to push an object, determining the power output of a machine, and measuring the work done by a person when performing physical tasks. It is also used in fields such as engineering, physics, and mechanics.

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