To alter the shape of an object, you must have a pair of equal but opposite forces. Forces that produce extension are known as tensile forces, whilst forces that produce compression are known as compressive forces. E.g a helical spring undergoes tensile deformation when tensile forces are exerted and compressive deformation when compressive forces are exerted.
The force extension graph of a helical spring is a straight line (from the origin) up to a point known as the elastic limit. In the linear region the spring undergoes elastic deformation (it will return to its original shape once the force is removed). Beyond the elastic limit, it undergoes plastic deformation - a permanent structural change and the spring will not return to its original shape once the force is removed.
Provided the force is less than the elastic limit, the spring obeys Hooke's law. Hooke's law states that the extension of the spring is directly proportional to the force applied. This is true as long as the elastic limit is not exceeded:
Where k is the force constant. A spring with a large force constant is difficult to extend whereas a spring with a small force constant is easy to extend. F=kx can also be applied for compression (where x represents the compression of the spring).
We need to know how to investigate Hooke's law...
This will produce a force extension graph. We need to know about force extension graphs in a little more detail (particularly the force-extension graphs of springs and wires). The area under a force extension graph is the work done. Firstly, it is important to realise that the loading and unloading curves of a force-extension graph may not be the same.
Metal wire
The loading graph follows Hooke's law until the elastic limit of the wire is reached. For forces less than the elastic limit the unloading curve will follow the same curve as the loading curve. However, if the elastic limit is exceeded the wire will undergo plastic deformation (see above) and the unloading curve will be parallel to the loading curve.
The force extension graph of a helical spring is a straight line (from the origin) up to a point known as the elastic limit. In the linear region the spring undergoes elastic deformation (it will return to its original shape once the force is removed). Beyond the elastic limit, it undergoes plastic deformation - a permanent structural change and the spring will not return to its original shape once the force is removed.
Provided the force is less than the elastic limit, the spring obeys Hooke's law. Hooke's law states that the extension of the spring is directly proportional to the force applied. This is true as long as the elastic limit is not exceeded:
F = kx
We need to know how to investigate Hooke's law...
- Attach a spring at one end using a clamp, boss, and clamp stand secured to the bench using a G-clamp/large mass
- Set up a metre rule with a resolution of 1mm close to the spring
- Suspend slotted masses from the spring
- Record the total mass added and the new length of the spring after each mass is added
- Repeat for at least 6 different masses
- Plot a graph of force against extension
This will produce a force extension graph. We need to know about force extension graphs in a little more detail (particularly the force-extension graphs of springs and wires). The area under a force extension graph is the work done. Firstly, it is important to realise that the loading and unloading curves of a force-extension graph may not be the same.
Metal wire
The loading graph follows Hooke's law until the elastic limit of the wire is reached. For forces less than the elastic limit the unloading curve will follow the same curve as the loading curve. However, if the elastic limit is exceeded the wire will undergo plastic deformation (see above) and the unloading curve will be parallel to the loading curve.
Rubber
Rubber bands do not obey Hooke's law. It will return to it's original shape if the force is removed however the loading and unloading curves are not the same. The characteristic 'loop' formed is known as the hysteresis loop. The area of this loop represents the thermal energy released when the material is loaded and then unloaded. It can also be seen that more work is done in loading (stretching) than unloading the rubber band.
Polythene
Much like rubber bands, polythene does not obey Hooke's law. Thin strips of polythene are very easy to stretch and suffer plastic deformation under relatively little force.
No comments:
Post a Comment