Let the spring be stretched through a small distance d x dx dx. Then work done in stretching the spring through a distance d x dx dx is **d W = F d x, dW=Fdx, dW=Fdx**, where F is the force applied to stretch the spring.

- Work Done Stretching a Spring. Work as Area: Formany springs, the force to stretch the spring is proportional to thedistance the spring is stretched (Hooke’s Law). This means that thegraph of force vs. position, in this case, will be a straight linepassing through the origin (F = 0 when stretch = 0). The area underthe force vs. position graph will be a triangle, which makes the workdone to stretch the spring
**easy to calculate**.

Contents

- 1 What is the work done in stretching the spring?
- 2 What is the formula of work done for stretching?
- 3 How do you calculate work done by Hooke’s Law?
- 4 How do you calculate work done?
- 5 How can we calculate the total work done in stretching the spring we can use several equivalent techniques?
- 6 How is work done on the spring different from work done by the spring?
- 7 How do you calculate work done by Young’s modulus?
- 8 Which equation serves to solve for the work done on a spring to stretch it to a certain position?

## What is the work done in stretching the spring?

Elastic potential energy is Potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched.

## What is the formula of work done for stretching?

In stretching a wire work is done against internal restoring forces. This work is stored as elastic potential energy or strain energy. If a force F acts along the length L of the wire or cross section A and stretches it by x then: Young′sModulus(Y)=StressStrain=F/Ax/L=FLAx⇒F=YALx.

## How do you calculate work done by Hooke’s Law?

The work done on the system equals the area under the graph or the area of the triangle, which is half its base multiplied by its height, or W=12kx2 W = 1 2 kx 2. W=Fappd=(12kx)(x)=12kx2 W = F app d = ( 1 2 kx ) ( x ) = 1 2 kx 2 (Method B in the figure).

## How do you calculate work done?

Work can be calculated with the equation: Work = Force × Distance. The SI unit for work is the joule (J), or Newton • meter (N • m). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.

## How can we calculate the total work done in stretching the spring we can use several equivalent techniques?

Question: How can we calculate the total work done in stretching the spring? We can use several equivalent techniques: • Summing the AW (Wotal = EAW). Finding the area under the curve of F vs. Xtotal • Using mathematical integration.

## How is work done on the spring different from work done by the spring?

As an aside, the work done by a spring and the work done on a spring are equal in magnitude and opposite in sign. So when a spring is streched by an external force and positive work is done on the spring, the work done by the spring (due to the reaction force in the spring) is negative.

## How do you calculate work done by Young’s modulus?

Find the work done in stretching a wire of length 2 m and of sectional area 1 mm² through 1 mm if Young’s modulus of the material of the wire is 2 × 10^{11} N/m². Given: Area = A = 1 mm² = 1 × 10^{–}^{6} m², Length of wire = L = 2m, Extension in wire = l = 1mm = 1 × 10^{–}^{3} m, Young’s modulus = Y =2 × 10^{11} N/m².

## Which equation serves to solve for the work done on a spring to stretch it to a certain position?

We can find the spring constant of the spring from the given data for the 4 kg mass. Then we use x = F/k to find the displacement of a 1.5 kg mass. The work that must be done to stretch spring a distance x from its equilibrium position is W = ½kx^{2}.