Procedure of finding force constant of a spring

Practical 3
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To find the force constant of a spring

Objectives:
To study the application of Hooke’s Law.
To study the forces in equilibrium.
To study the resolution of vector quantities.

Apparatus and Materials:
1. Spring
2. Plumb-line
3. Protractor
4. Slotted masses 100g with hanger
5. Thread
6. Retort stand
7. Nail or pin

Setup:
1. Set up the apparatus as shown in Figure 4-1 below.
2. Adjust the spring, so that it stretches horizontally.
3. The angle between the plumb-line and the section AB is θ.
4. The mass of the load is m, its weight is mg.

Figure 4-1

Theory
Let:
g = 9.80 ms-2 m = mass of the load θ = angle between the plumb-line and the section AB x = extension of the spring k = force constant of the spring l = stretched length of the spring lo = unstretched length of the spring

When the system is in equilibrium, the forces acting at the point B are in equilibrium

Vertically: mg = T cos θ…………. (1)

Horizontally: kx = T sin θ…………... (2)

Therefore: kx = mg tan θ

A graph of x against tan θ will yield a straight line.

The gradient is equal to.

Procedure:
1. Measure the unstretched length, lo of the spring before setting up the apparatus.
2. Adjust the spring, so that it stretches horizontally.
3. Measure the angle θ between the plumb-line and the section AB.
4. Measure the new length, l of the spring.
5. Calculate the extension, x of the spring. [where x = l – lo]
6. Pull the spring side way to vary the length l to obtain eight (8) sets of values of θ and x. {Note: before taking the value of the angle θ, make sure that the spring is horizontal.}
7. Tabulate: x, θ, tan θ.
8. Determine the gradient of the graph.
9. Determine the force constant, k of the spring.