Fizyka - program rozszerzony I
Review the key concepts, equations, and skills for spring potential energy and Hooke's law. Understand how to analyze a spring force vs. displacement graph.
|Spring||Object that can extend or contract and return to the original shape.|
|Spring constant (||Measure of a spring’s stiffness, where a more stiff spring has a larger |
|Spring force (||Force applied by a spring given by Hooke’s law. SI units of |
|Elastic potential energy (||Potential energy stored as a result of applying a force to deform a spring-like object. SI units of |
|Equation||Symbols||Meaning in words|
|The magnitude of the force required to change the length of a spring-like object is directly proportional to the spring constant and the displacement of the spring.|
|Elastic potential energy is directly proportional to the square of the change in length and the spring constant.|
The force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring for small distances. The force exerted back by the spring is known as Hooke's law
is the force exerted by the spring, is the displacement relative to the unstretched length of the spring, and is the spring constant.
The spring force is called a restoring force because the force exerted by the spring is always in the opposite direction to the displacement. This is why there is a negative sign in the Hooke’s law equation. Pulling down on a spring stretches the spring downward, which results in the spring exerting an upward force.
How to analyze a spring force vs. displacement graph
The area under the force in the spring vs. displacement curve is the work done on the spring. Figure 1 shows a plot of force on the spring vs. displacement, where displacement is
when the spring is unstretched. The work done on a spring stores elastic potential energy in the spring until the spring goes back to its original length. Therefore, is equal to the work done and also to the area under the curve.
The area is a triangle with the following equation:
Note that the spring constant
is the slope of the line since .
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Although the spring force is a restoring force and has a negative sign, the elastic potential energy
cannot be negative. As soon as the spring is stretched or compressed, there is positive potential energy stored in the spring.
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To check your understanding and work toward mastering these concepts, check out the exercise on calculating spring force and the exercise on calculating elastic potential energy.