Area under force vs displacement graph :D?

In summary, the conversation discusses how to find the value of K at 4m, given the F.s graph and Kinitial = 2J. The solution involves finding the area under the graph using the equation W=F.d, and then using the equation W=Kf-Ki to solve for Kf. The final answer is 6J.
  • #1
DK_sam
2
0

Homework Statement


Find K at 4m, besides the F.s graph they also give me Kinitial = 2J

Homework Equations


W=F.d and W=Kf- Ki

The Attempt at a Solution


The first thing I did was to find the area under the graph.
1/2(4)(2)=4J W=F.d so that's my work.
Then I replaced that 4J into the other eq W= Kf-Ki
then solved for Kf.
W+Ki=Kf
plugging in values 4j +(2J)=Kf
then 6J=Kf
Is that correct guys? Thanks for your help!
 

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  • #2
DK_sam said:

Homework Statement


Find K at 4m, besides the F.s graph they also give me Kinitial = 2J

Homework Equations


W=F.d and W=Kf- Ki

The Attempt at a Solution


The first thing I did was to find the area under the graph.
1/2(4)(2)=4J W=F.d so that's my work.
Then I replaced that 4J into the other eq W= Kf-Ki
then solved for Kf.
W+Ki=Kf
plugging in values 4j +(2J)=Kf
then 6J=Kf
Is that correct guys? Thanks for your help!
looks good! Always put a space between the numerical value and the unit, 6 J not 6J.
 
  • #3
Thank you good sir! I will next time! :D good night!
 

1. What is the significance of the area under a force vs displacement graph?

The area under a force vs displacement graph represents the work done by the force. It is a measure of the energy transferred to an object as it is displaced by a force.

2. How is the area under the graph calculated?

The area under the graph can be calculated by finding the total sum of all the small rectangles formed by the force and displacement values. This can be done using numerical integration techniques such as the trapezoidal rule or Simpson's rule.

3. What does a large area under the graph indicate?

A large area under the graph indicates that a greater amount of work has been done by the force on the object. This could mean that the object has experienced a larger displacement or a greater force acting on it.

4. How does the shape of the graph affect the area under it?

The shape of the graph can greatly affect the area under it. A steeper slope indicates a higher force and can result in a larger area. Similarly, a longer graph represents a larger displacement and can also lead to a larger area.

5. Can the area under a force vs displacement graph be negative?

Yes, the area under the graph can be negative. This occurs when the force is acting in the opposite direction of the displacement, resulting in negative work being done on the object. The area under the graph in this case would represent the magnitude of the negative work.

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