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16.1 Hooke's Law: Stress and Strain Revisited

- The plastic ruler moves back and forth when it is displaced from its equilibrium position.
- There is a force to the right when the ruler is on the left.

- The first law suggests that an object is moving.
- Without force, the object would move in a straight line.
- When the restoring force is released, it causes the ruler to move back toward its equilibrium position, where the net force on it is zero.
- By the time the ruler gets there, it gains strength and continues to move to the right.
- The process is repeated until dissipative forces stop the motion.

- The forces reduce the motion until the ruler comes to rest.

- When the restoring force is proportional to displacement, the simplest oscillations occur.

- The restoring force is in the opposite direction to the displacement.

- The ruler is stopped and moved back to equilibrium.
- The motion will repeat itself from there.

- The units are N/m.
- It's related to Young's modulus when we stretch a string.
- The force constant is equal to the slope of the graph.
- If they follow Hooke's law and measure restoring forces created by springs, they can calculate force constants.

- The system obeys Hooke's law if the graph is straight.
- The force constant is the slope of the graph.
- The weight is supported if the mass is stationary.

- The car's suspension system is affected by this.

- The equilibrium position of the car should be considered before someone gets in.
- The car is displaced to a position after it settles down.
- The springs give a force equal to the person's weight.
- This force is in Hooke's law.
- We can solve the force constant if we know.

- The restoring force is up and the displacement is down because they are in opposite directions.
- If the person got in the car without shock absorbers, it would spin up and down.
- Bouncing cars are a sign of bad shock absorbers.

- Work must be done in order to make a change.
- The force must be exerted through a distance, whether it's a guitar string or a car spring.
- If the only result is a change in shape, then all the work is stored in the object as potential energy.
- The potential energy is stored in a spring.
- We generalize the idea to elastic potential energy for any system that can be described by Hooke's law.

- It is possible to find the work done in order to find the energy stored.
- The work is done by an applied force.
- The restoring force is opposite to the applied force.
- Work done on the system is force multiplication by distance, which shows the area under the curve.
- One way to determine the work is to note that the force increases linearly from 0 to, so that the average force is, and thus (Method B in the figure).

- A graph of applied force versus distance for a system that can be described by Hooke's law is displayed.
- The area under the graph or the area of the triangle, which is half its base, is the work done on the system.

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