Conservative Forces

How do you find the energy stored in a spring that does NOT follow Hooke’s law?

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How does the work done by a conservative force compare to the change in potential energy caused by the same force? Select two correct answers.

• When the force does negative work, the potential energy of the object decreases.

• The potential energy of the object increases when the force does negative work.

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If a conservative force does positive work on an object, what happens to the speed of that object?

• Increases

• Decreases

Which of the following statements are true about conservative and non-conservative forces?

• A force is regarded as a non-conservative force if it does not add mechanical energy to a system of objects.

• The force of gravity and elastic (spring) force are both examples of a conservative forces.

• None of these

• Physicists envy biologists' ability to instill order on the world of animal species through their taxonomic system. So physicists have made a habit of identifying forces as conservative and non-conservative forces in order to instill order on the world of forces.

The toy car is pushed up against the spring and released. If it follows the purple path, it makes it to the top of the hill and comes to rest. If the car compresses the spring the same amount and is then released to follow the alternate path, it will make it to the top of the hill and come to rest as well. Why?

• In the absence of non-conservative forces the energy transformations required are path independent

• The statement is incorrect. It is not possible for the car to reach the top of the hill using the alternate path

• Only non-conservative forces act on the car as it moves through either path

A constant force F pushes a particle through a displacement

r . In which of these three cases does the kinetic energy of the particle decrease?

• A

• B

• C

• Both A and B

• Both A and C

The area under the curve on a conservative force versus displacement graph tells you--

• the amount of work done on an object

• the change in energy for an object

• both the work done and the change in energy because work = change in energy according to the work-energy theorem

The following graphs, all drawn to the same scale, represent the net force F as a function of displacement x for an object that moves along a straight line. Which graph represents the force that will cause the greatest change in the kinetic energy of the object from x = 0 to x = x₁?

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A 10‑kilogram body is constrained to move along the x‑axis. The potential energy U of the body in joules is given as a function of its position x in meters by

U(x) = 8x³ ‑ 6x² + 4

The force on the particle at x = 2 m is

• 44 N in the +x direction

• 44 N in the -x direction

• 72 N in the +x direction

• 72 N in the -x direction

• 98 N in the +x direction

For a particular nonlinear spring, the relationship between the magnitude of the applied force F and the resultant displacement x from equilibrium is given by the equation F = kx². What is the amount of work done by stretching the spring a distance x_o ?

• kx_o³

• ½ kx_o

• ½ kx_o³

• 1/3 kx_o²

• 1/3 kx_o³