Question

What does the slope of force versus displacement graph represent?

Answer 1

Hint: We know that slope is the ratio of change in y component to the change in x component. Here we will first brush up our concept of force and displacement and then will see what the slope of force versus displacement graph represents.

Complete step by step answer:
First we will know what is meant by force then will know about displacement and then we will define the relation between force and displacement. Force is any interaction that can change the motion of an object. Force is a vector quantity (i.e. it has both magnitude as well as direction). SI unit of force is newton.

The displacement is the linear distance between the initial position and the final position of that moving body. A straight line drawn between two points is of least length among all curves joining the two, so, the linear distance between two points is the least length of path to be travelled between two points. So, we can say, that distance when it is shortest, becomes displacement.

The magnitude of the force required to change the length of a spring-like object is directly proportional to the displacement of the spring and the spring constant. The relation between force and displacement of the spring is given by $F=-k\Delta x$ which is also known as Hooke’s law. Where, $F$ is the Force applied on the spring, $k$ is the spring constant and $\Delta x$ is the displacement of the spring from a neutral position.

If the neutral position is 0, then the displacement $\Delta x=x-0=x$. When we plot the graph $F$ vs $\Delta x$, we get the slope $k$. Therefore the slope of the spring force $F$ vs. $x$ is the spring constant $k$. The graph will be a straight line in the fourth quadrant with negative slope equal to negative of force constant.

Note: Another thing to keep in mind is that the area under the graph of force vs displacement is the work done by the relation between force, work done and displacement is given by $W=F\cdot \Delta x$ Where, $W$ is the work done, $F$ is the force and $\Delta x$ is the displacement.