Hooke's Law Notes

HOOKE’S LAW

The law states that within the elastic limit, the extension caused by a force in a spring is proportional to the force acting on the spring.

Mathematically this law can be represented as; F ∞ x (where F is the force and x is the extension) F = k x where k is a proportionality constant called spring constant and it is unique to the material of the spring. Rearranging, k = F/x The spring loses its springiness when the force is too large; we say that the spring has crossed its elastic limit. The extension, x is found using the formula x = (New length of the spring – the original length of the spring).

Hooke’s Law – Plots loadVsextension

In this case, gradient = F / x load /N

Remember k = F / x Hence, k = gradient elastic limit y2 – y1 gradient = x – x = F / x 2 1

extension/cm

extension Vs load

In this case, gradient = x / F extension / cm

Remember k = F / x Hence, k =1/ (gradient)

load / N

elastic limit y2 – y1 gradient = x – x = x / F 2 1

The above plots involve the quantities load (force) and extension. However, if the plot involves load and length of spring instead of extension, the plot does not start at the origin.

spring length / cm

extension Vs load

load / N

actual spring length

elastic limit

WORKSHEET 1. In an experiment, forces are applied to a spring as shown in Fig. a. The results of this experiment are shown in Fig b.

(a) What is the name given to the point marked Q on Fig.b _______________________________________ (b) For the part OP of the graph, the spring obeys Hooke’s Law. State what this means. _______________________________________________________________________________________ _______________________________________________________________________________________ (c) The spring is stretched until the force and extension are shown by the point R on the graph. Compare how the spring stretches, as shown by the part of the graph OQ, with that shown by QR. _______________________________________________________________________________________ _______________________________________________________________________________________ (d) The part OP of the graph shows the spring stretching according to the expression F = kx. Use values from the graph to calculate the value of k. _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________

2. The following results are obtained for a spring stretching experiment. Spring length /mm

40

44

48

52

56

60

64

72

86

Load /N

0

1

2

3

4

5

6

7

8

Extension /mm

(a) Complete the table. (b) Plot an extension Vs load graph for the given values. (c) Plot a length of spring Vs load graph for the given values. (d) Plot a load Vs extension for the given values. (e) Calculate the slope of the graph in each case. (f) Mark the elastic limit and calculate the value of spring constant in each case.