Physics Lesson 4.4.3 - The Graphical Representation of Hooke's Law. Limit of Elasticity

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Welcome to our Physics lesson on The Graphical Representation of Hooke's Law. Limit of Elasticity, this is the third lesson of our suite of physics lessons covering the topic of Types of Forces III (Elastic Force and Tension), you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

The Graphical Representation of Hooke's Law. Limit of Elasticity.

The equation (1) written in the scalar form, i.e. F_e = k × x shows a linear function whose graph is a slope that starts from the origin like the one shown in the figure below.

As long as the graph is linear, the elastic object involved (spring, rubber band etc.) shows a perfectly elastic behaviour. Therefore, the spring obeys the Hooke's law. However, when the pulling force is too large, the spring may not return to its original position. We say the force used has exceeded the limit of elasticity. For example, some dynamometers don't show anymore the value zero when they are not in use because heavy objects that exceed the limit of elasticity have been hanged on them.

When the object hanged is too heavy, the spring breaks into two pieces. The breaking point is represented through the letter B in the graph above.

Example 2

The elastic force vs deformation graph for a spring is shown in the figure below.

1. What is the value of the spring constant in N/m?
2. What is the minimum force to be used so that the spring does not turn again to its original position?
3. What is the minimum force needed to break the spring in two pieces?

Solution 2

1. The spring constant is calculated considering only the part OA of the graph as only in this part the Fe vs x graph is linear, i.e. it obeys the Hooke's Law.
   Since the graph is linear, we can take two points on it and calculate the slope as discussed in the Kinematics chapter when we calculated the instantaneous velocity. For simplicity, we can take the origin O and the point A (at the origin the spring is unstretched). Thus, we have:

2. The minimum force to make the spring permanently loose its elastic properties is shown at the point A in the graph. The corresponding value of the elastic force in that point is 70 N. This value represents the elastic limit of the spring.
3. The spring breaks at the point B as there is no more graph after this point. The corresponding value of the force is 80 N. This means when a 80 N force is used in the spring, it breaks in two pieces.

You have reached the end of Physics lesson 4.4.3 The Graphical Representation of Hooke's Law. Limit of Elasticity. There are 4 lessons in this physics tutorial covering Types of Forces III (Elastic Force and Tension), you can access all the lessons from this tutorial below.

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