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Elasticity and Hooke's Law If a force is exerted on an object, such as the vertically suspended metal rod shown in Figure 3.1, the length of the object changes Experiments show that Al is proportional to the force exerted on the object.If the object is stretched beyond the elastic limit, o It enters the plastic region: it does not return to the original length upon removal of the external force, but remains permanently deformed o The maximum elongation is reached at the breaking point.Figure 3.2 shows a typical graph of applied force versus elongation.: o Up to a point called the proportional limit, Eq. 3.1 is a good approximation for many materials, and the curve is a straight line.For if the force is too great, the object stretches excessively and eventually breaks.

Elasticity and Hooke's Law
If a force is exerted on an object, such as the vertically suspended metal rod shown in Figure 3.1, the length of the object changes Experiments show that Al is proportional to the force exerted on the object. This proportionality can be written as an equation
Figure 3.1 Hooke's law Al o applied force
F = kAl
3.1
Here, F: represents the force pulling on the object,
Al: is the change in length,
k: is a proportionality constant.
Eq. 3.1, which is sometimes called Hooke's law, is found to be valid for almost any solid material from iron to bone-but it is valid only up to a point. For if the force is too great, the object stretches excessively and eventually breaks.
Figure 3.2 shows a typical graph of applied force versus elongation.:
• Up to a point called the proportional limit, Eq. 3.1 is a good approximation for many materials, and the curve is a straight line.
• Beyond this point, the graph deviates from a straight line, and no simple relationship exists between F and Al.
• up to a point farther along the curve called the elastic limit, the object will return to its original length if the applied force is removed
• The region from the origin to the elastic limit is called the elastic region.
If the object is stretched beyond the elastic limit,
• It enters the plastic region: it does not return to the original length upon removal of the external force, but remains permanently deformed
• The maximum elongation is reached at the breaking point. The maximum force that can be applied without breaking is called the ultimate strength of the material.