Elastic Potential Energy

Transcription

1 Elastic Potential Energy

2 If you pull on a spring and stretch it, then you do work. That is because you are applying a force over a displacement. Your pull is the force and the amount that you stretch the spring is the displacement. Since work is the transfer of energy, we must understand where the energy was transferred. We say that the energy was transferred into the spring. The work becomes stored energy in the spring. The work becomes potential energy in the spring. A spring can be stretched or compressed. The same mathematics holds for stretching as for compressing springs. We will be primarily discussing energy as it is stored in a spring when it is stretched here; however, the same physics would apply for a spring when it is compressed.

3 Work and Energy Objects like rubber bands and springs that return to their original size and shape after being distorted are said to be elastic. Stretching a spring requires work. This work is stored in the stretched spring in the form of potential energy. The potential energy stored in a distorted elastic material is referred to as elastic potential energy.

4 Work and Energy When a spring is stretched by a distance x, the force exerted on the spring increases uniformly from 0 to kx, where k is the spring constant. Thus, the average force is exerted on the spring is. Since the average force is, the work done in changing the length of the spring is the average force times the distance, or This work is stored as elastic potential energy.

5 Work and Energy The spring constant, k, is a measure of the stiffness of a spring (large k stiff spring, small k soft spring).

6 Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is: where is a constant factor characteristic of the spring, its stiffness. (F=kx)

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9 Work and Energy

10 Example 1: If the force to stretch a spring is given as F = (100 N/m)x, then what is the potential energy of the spring if it is stretched 2 meters from rest? Solution: Here k = 100N/m and x = 2 m. Therefore: PEE = (1/2)kx2 = (1/2)(100N/m)(2 m)2 = 200 Joules

11 Example 2: It takes a force of 20 Newtons to hold a spring stretched to a distance of 40 cm. What is the elastic potential energy of the spring at this position? Solution: We know that F = 20 N, when x = 40 cm = 0.40 m. Since F = kx, then k = F/x = (20 N)/(0.40 m) = 50 N/m. Now, PEE = (1/2)kx2 = (1/2)(50 N/m)(0.40 m)2 = 4 Joules.

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13 Conservation of Energy

14 Conservation of Energy Energy takes many forms: mechanical, electrical, thermal, and nuclear. Any time work is done, energy is transformed from one form to another. One process might transform some kinetic energy into electrical potential energy; another might transform some spring potential energy into kinetic energy.

15 Conservation of Energy However. no matter what the process, the total amount of energy in the universe remains the same. This is what is meant by the conservation of energy. To say that energy is conserved means that energy can never be created or destroyed it can only be transformed from one form to another.

16 Conservation of Energy When frictional forces act on a system, such as when a car's brakes are applied, kinetic energy is transformed into thermal energy.

17 Conservation of Energy In situations where all forms of friction can be ignored, no potential or kinetic energy is transformed into thermal energy. In this ideal case, the sum of the kinetic and potential energies is always the same. The sum of the kinetic and potential energies of an object is referred to as its mechanical energy. Thus, mechanical energy = potential energy + kinetic energy E = PE + KE This means that mechanical energy is conserved.

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20 Mechanical Energy Mechanical energy is due to the position and motion of the object. What happens to the mechanical energy of an apple as it falls from a tree?

21 Mechanical Energy As the apple falls to the ground, its height decreases. Therefore, its GPE decreases. The potential energy is not lost it is converted into kinetic energy as the velocity of the apple increases. What happens to the mechanical energy?

22 Mechanical Energy The mechanical energy does not change because the loss in potential energy is simply transferred into kinetic energy. The energy in the system remains constant!!

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25 Conservation of Energy Energy conservation may be used to solve many physics problems. For example, energy conservation may be used to find the final speed of a set of keys dropped to the floor from a height h (see figure below). By equating the initial potential energy at the top (mgh) to the final kinetic energy at the bottom and solving for the speed of the keys at the bottom, we find

26 Conservation of Energy Changing the initial speed of a downward moving object by a small amount can result in a relatively large increase in final speed.

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