How do you calculate the work needed to stretch a spring?

How do you calculate the work needed to stretch a spring?

The blue line represents the graph of F = kx (Hooke’s Law). We know that the area shaded in red represents the work you would need to do to stretch the spring a distance x from its rest position. Since this area is a triangle, the shaded area = (1/2)(base)(height) = (1/2)(x)(kx) = (1/2)kx2.

What is the limit of proportionality of a spring?

Spring constant is a measure of the stiffness of a spring up to its limit of proportionality or elastic limit. The limit of proportionality refers to the point beyond which Hooke’s law is no longer true when stretching a material.

What is extension of a spring?

When an object, such as a spring, is stretched, the increased length is called its extension. Hooke’s law: The extension of a spring is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.

What is the unstretched length of the spring?

We know from the question that the unstretched length of the spring is 3 m. That would mean the spring stretched by 2 m (5 m – 3 m = 2m) after the block was hung at ring A. We can now figure out the force of spring AB using Hook’s Law. Let us now draw our free body diagram.

How long will a spring stretch?

Hooke’s Law tells us that the extension of the spring is directly proportional to the stretching force:

1. F=kx.
2. F=mg=0.04×9.81=0.3924N.
3. ∴ 0.3924=30×x.
4. x=0.392430=0.01308m.
5. 0.20+0.01308=0.21308m.
6. =21.3cm.

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 much work is done in stretching a spring of spring constant k from its unstretched?

When a spring with spring constant k is stretched by distance L from its unstretched length L0 by an external force acting parallel to the string (figure a), the work done by the external force is W=(1/2)kL2. This work equals the potential energy of the stretched spring.

How to calculate the mass of a spring?

Solution: The spring mass equation for free motion is mx00= kx: We solve for kusing the same strategy above, k= : To write the mass of the spring we convert weight Wto mass using, m= W g = 2 lbs 32ft/s2

What is the relationship between Hooke’s law and spring constant?

Hooke’s law and spring constant. Hooke’s law deals with springs and their main property – the elasticity. Each spring can be deformed (stretched or compressed) to some extent.

Can you calculate the force of a compressed spring?

You can calculate anything, in any order. We created the Hooke’s law calculator (spring force calculator) to help you determine the force in any spring that is stretched or compressed. You can also use it as a spring constant calculator if you already know the force.

How to find the elastic potential energy of a spring?

You can find the elastic potential energy of the spring, too. Choose a value of spring constant – for example, 80 N/m. Determine the displacement of the spring – let’s say, 0.15 m. Substitute them into the formula: F = -kΔx = -80 * 0.15 = 12 N. Check the units! N/m * m = N.