Hook’s Law.

This was enunciated by **Robert Hooke** in the 17th Century. It deals with the deformation of solid materials due to unbalanced external forces, such as stretching and compression.

The images show that a spring can either compressed or stretched. In both cases the length of the spring changes. The difference between the original length of the spring and the changed length will give the change in length. According to hooke’s law this change is directly proportional to the applied force.

The graph shows how the extension of a spring has changed according to the change of pulling force. The straight line graph up to about 7.5 N shows that the extension or stretch is directly proportional to the applied force.

Beyond that the spring does not obey the Hook’s

Spring Constant

Force/N | 1 | 2 | 4 | 5 | 6 | 7 | 8 |

Stretch /mm= x | 2 | 4 | 6 | 10 | 12 | 14 | 18 |

Force /stretch k | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | o.44 |

Stretch | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 18 |

k | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.44 |

Str x k | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 7.92 |

This agrees with the formula Force = a constant x Stretch

F = k x x

The constant k is called the SPRING CONSTANT

This is true only up to the elastic limit.

We can re write the formula as k = F / x

Here although we calculated in milimeters normally the unit given is **newton per meter**.

.

**Elastic Potential Energy**

If
a spring having a spring constant of 0.5
showed an extension of 3 cm what is the elastic energy stored in the
spring?

Energy
is equivalent to work done.

W
= Force x extension.(x)

F
= *k *x extension.(x) As the force starts from zero the average force becomes F
/2.

W = ½ *k*x^{2} .

**Potential energy** **= ½ ***k*x^{2}

^{}

**1.0**

A spring 0.10 m long extends by 0.03 m for a force of 5 N.

Find the following:

1.1 The length of spring if the force is doubled.

1.2 The spring constant.

**2.0**

All the springs shown here are identical. The length of a spring in the absence of a load is 10 cm.

2.1 What is the length of a spring in A system?.

2.2 What is the length of a spring in B system?

2.3 After an investigation a student found the length of a spring slightly different from the calculated value. What could be the reason for this?

**3.0 ** A ball is hanging from spring which has a spring constant of 6.0 Nm-1, The extension of the spring from original length is 0.10m.

Find the following:-

3.1 The mass of the ball.

3.2 Potential energy gained by the spring.

**4.0 **

The length of a spring with two different loads is shown in the diagram.

Find the following:-

4.1 The real length of the spring.

4.2 The elastic limit.

4.3 The spring constant.

**5.0**

A car has a weight of 9800 N. Assume that the force gets distributed equally on 4 shock absorber. Each shock absorber has a length of 0.4 m which has to compress by 0.08 m. What is the spring constant?

For answers click:- Answer page- Physics A to K