Deformation of Solids
DEFORMATION OF SOLIDS
What is Hooke’s law?
Provided that an objects elastic limit is not exceeded, the extension of the object is proportional to the force applied (load).
What is meant by spring constant?
The force per unit extension of the spring
Formula:
Compressive force: Describes a tightening force that can shorten an object.
E.g.: The sponge has an elastic structure, that is why it can regain its original shape as soon as the effect of external force is worn away. When a force is applied to both ends of the sponge, the sponge tends to compress, and the original size of the sponge is reduced. Therefore, a compressive force is said to be present.
Tensile force: The stretching forces acting on a material.
E.g.: Tug of war is one of the most popular sports among young people that uses tension. The basic requirement of tug of war is that the rope be taut. Two teams trying to pull the rope towards themselves is the basis of tug of war. The force present in the rope when pulling is applied from both ends is the tension in the rope. Without tension, no one can win the game.
Limit of proportionality: The point beyond which an object no longer obeys Hooke’s law and is unable to revert to its original shape or size.
Elastic limit: The maximum value of stress to which a solid can be stretched without a permanent change in size or shape.
What is stress?
force per unit area within materials due to external force.
Formula:
What is strain?
The measure of how much an object is stretched or deformed.
Formula:
What is meant by young modulus?
Young’s modulus is a property of a material that tells us how easily it can be stretched and deformed and is defined as the ratio of the tensile stress to the tensile stress.
It is defined as the stress in a material divided by the strain.
Formula:
Worked E.g.:
Young modulus experiment:
1. Measure the diameter of the piece of wire with a micrometer screw gauge. Take repeated measurements and calculate the average diameter of the wire.
2. Clamp one end of the wire in between 2 wooden blocks and to the bench with a G-clamp. Must be tightly clamped.
3. Tie the wire around the wooden blocks so it can support the load when applied.
4. Attach the pulley to the opposite end of the bench and have the wire hang over it so that it hangs just over the pulley.
5. Place a small piece of tape on the wire anywhere from 20-25 cm from the pulley. This acts as the marker for the end of the section of the wire you are considering.
6. Make sure the wire is taut. If not, add a small weight at the end of the wire to straighten it out.
7. Measure the unstretched length of the wire from the end of the wire clamped to the bench (wooden blocks) to the tape marker.
8. Attach a tape measure or a meter rule to the table just below the wire so you can measure its extension as loads are added.
9. Add a mass of 0.5 or 1 kg to the end of the wire. After a brief while, measure the extension of the wire.
10. Continue to increase the load and for each load measure the extension of the wire. Continue until you have multiple sets of readings.
Elastic deformation: When an object returns to its initial form when force is removed.
E.g.: When the rubber band is stretched, it will feel a force that can reduce any type of deformation. The force generated when the rubber band is deformed is the reaction force against the external force, which is called elastic force. The elastic force generated in the elastic body helps the body resist any changes in shape and will disappear once the external force is removed.
Plastic deformation: When an object is incapable of returning to its initial form when force is removed. Object is deformed permanently.
E.g.: When an external force is applied to a pencil, it tends to break into pieces. This happens because pencils are inherently inflexible and therefore do not have great ability to handle large amounts of force and pressure. Therefore, when a deforming mechanical force having a relatively high magnitude is applied to a pencil for a long time, it will deform.
What is elastic potential energy?
Energy stored in a body as a result of applying a force to change objects shape or size.
E.g.: An archer’s bow with the string pulled back, A coiled spring, A stretched rubber band, basically anything that is forced out of its shape that wants to return to its original form has elastic potential energy.
Formula:
Work done: Product of the force and the distance moved in the direction of the force.
Worked E.g.:
Derivation of elastic potential energy:
