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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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