HOOKS LAW: STRETCHING OF MATERIALS.

Stretching of materials.

• The forces between molecules in a solid account for its characteristic elastic or stretching properties. When a solid is stretched, the spaces between its molecules increase slightly.
• The tension felt in the stretched rubber band is due to all the forces of attraction between molecules in it.
• The extension produced on a material depends on;

1. The nature of the material.
2. The stretching force
3. The cross- section area of the material.
4. Its original length.

The forces between molecules in a solid account for its characteristic elastic or stretchy properties. When a solid is stretched, the space between the molecules increase slightly e.g. tension felt in a rubber band is due to all forces of attraction between molecules in the rubber band.

Hook’s law.

It states that the extension of an elastic body or material is directly proportional to applied force provided that the elastic limit is not exceeded.

                        F = k  e     where k is a constant called elastic constant and elastic constant depends on the material

EXP:TO INVESTIGATE THE STRETCHING OF A SPIRAL SPRING.

Apparatus.

1. Spiral spring.
2. Clamp and stand.
3. Meter rule.
4. Several moses.

Procedure.

1. Suspend the spring using the clamp and stand.
2. Place the meter rule next to the spring such that the pointer of the spring touches the scale.
3. Note the pointer readings ________ cm.
4. Suspend a 20g mass and note the new reading _____________cm.
5. Calculate the extension. E= reading2 – reading1
6. Calculate the force. F= mg x 10 to convert the force to newtons
7. Repeat the experiment using different masses and draw a graph of extension against force.

Results.

1. The graph is a straight line passing through the origin.
2. The extension of the spring is directly proportional to the stretching force.
3. The slope of the gradient of the graph represents the elastic constant or spring constant.

                                    F= ke     SI units is N/m

4. The area under the graph represent the energy stored in the spring or the work done in stretching the spring.

                        E= ½ fe   work done = ½ fe        Units is joules (J)

• This is called elastic potential energy.

Example.

1. A mass of 100g is suspended from the lower end of the spring. If the spring extended by 100 cm and the elastic limit of the spring is not exceeded, calculate
2. The spring constant.

F= ke

K= f/e

K= 1N/0.1m =10N/m

1. The energy stored in the spring.

E= ½ fe

E= ½ x 1x 0.1

E= 1/20         = 0.5J

2. A piece of wire of length 12cm is stretched through 2.5 cm by a mass of 5kg. Assuming that the wire obeys hooks law, calculate
3. The length that a mass of 12.5kg stretches the wire.

1. The force that will stretch it through 4 cm.

Arrangement of springs.

• Springs can be arranged in parallel or series.

1. Series arrangement.

• 2 or more springs can be arranged in series
• The total extension is the sum of each spring e.g.

Three springs are arranged in series and support a load of 20N. Determine

1. The total extension.
2. The spring constant of each spring.
3. The spring constant of the system.
4. The extension of the spring.

   2. Parallel arrangement.

Two or more springs can be arranged in parallel.

The total extension is the extension of one spring divided by the number of springs as they share the weight of the support e.g.

Three springs are arranged as in the figure below and support a load of 200N. If the extension of one spring while supporting the same load is 4 cm, determine

1. The total extension.
2. The spring constant of the combination.

                        Spring stretched beyond elastic limit.

If a body or elastic string is stretched beyond elastic limit, it undergoes permanent deformation, if further stretched, it breaks.

A graph of force against extension shows what happens.

OA → The graph is a straight line, force is directly proportional to extension.

            The body returns to its original shape and size when the force is removed.

A → It is the elastic limit.

Fo is the maximum force.

Eo is the maximum extension the spring can undergo.

          Beyond this limit, the material does not return to its original shape and size.

AB → The body suffers permanent deformation.

                                                Compressing force.

When 2 ends of a spring are squeezed together, it shortens/reduces its length.

The compression increases with increase in force.

A graph of compressing force against compression.

OA → The spring obeys hooks law.

             After point A, the compression remains constant as the force reduces. Beyond this poin, no change in length.

If the spring is further compressed beyond B, it is permanently destroyed.

The length increases with increase in compressing force.

                                                Compressing force and length.

Point A is the maximum force/ minimum length where the turns of the spring are virtually pressing onto one another. Beyond this point, there is no noticeable increase in length.

Fo is the maximum force that can be applied to the spring and Lo is the minimum length the spring can be compressed.