In a Force vs Distance graph, is work the area underneath?

In summary: The equation W = Fcos(\theta)\Delta x is used to find the work done by a constant force. From 0 to 0.06m, the force varies, and this is why we use the interval method.
  • #1
carmenn
4
0
1. Homework Statement

In a Force vs Distance graph, is work the area underneath?
A person pushes a shovel into the ground to do some spring gardening. He applies a force to the shovel over the following displacement.

0 N - 0 m
4 N - .02 m
8 N - .04 m
12 N - .06 m

Draw a graph, and find work done by man on shovel over the .06 m. 2. Homework Equations
F x d = W

The Attempt at a Solution


So at first, I calculated all the work, using F x d, and added all of them together, but he said that was wrong. And after we multiplied each of the the force by .02 since its in intervals and then added, but apparently we were wrong again. We have drawn a graph, that is a straight line. Is the area underneath the work? If so, why? Thanks
 
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  • #2
Yes, the area underneath the graphed line is the work, tho' you should be using the x-axis for the distance, and the y-axis for the force(that's simply the common convention). Can you show me how you arrived at yoru answer?
 
  • #3
why is distance on the x axis?

well, if i use the area under the graph, then it'd be

distance x force / 2

.06 x 12 / 2

.36 J

But can someone explain why? Since i had come up with 1.12 J when adding them all together, and .48 J when using the interval method
 
  • #4
I'm not particularly sure how you came up with 0.36J and 1.12. Can you show me how you arrived at those answers both mathematically and with words? Keep in mind that the equation [tex] W = Fcos(\theta)\Delta x [/tex] is used to find the work done by a constant force. From 0 to 0.06m, the force varies, and this is why we use the interval method. Does that make sense?
 
  • #5
I'm actually not sure what I did, but after reading what you wrote and doing a bit of asking around, I finally have the answer. Thank you for your help! Much appreciated!
 

1. What does a Force vs Distance graph represent?

A Force vs Distance graph represents the relationship between the applied force on an object and the distance it moves in response to that force.

2. How is work calculated from a Force vs Distance graph?

The work done on an object is equal to the area underneath the Force vs Distance graph. This can be calculated by finding the area of each individual shape formed by the graph and adding them together.

3. What is the significance of the area underneath the Force vs Distance graph?

The area underneath the graph represents the amount of energy transferred to the object in the form of work. This is because work is defined as the product of force and distance, and the area represents the product of the two quantities.

4. Can a Force vs Distance graph have a negative area?

Yes, a negative area underneath the graph indicates that work is being done on the object by an external force, instead of the object itself doing work. This can happen when the applied force is in the opposite direction of the object's motion.

5. What other information can be determined from a Force vs Distance graph?

Aside from work, a Force vs Distance graph can also give information about the object's displacement, velocity, and acceleration. It can also show the amount of force required to move the object a certain distance.

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