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Physics Unit 4 Work and Energy Study Guide
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An object possesses kinetic energy by moving.
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Interactions with other objects can create potential energy.
So an object cannot “have” potential energy, although that is a common way to
explain potential energy.
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Gravitational potential energy is energy stored in a gravitational field.
When an object is near the surface of a planet, the formula is:
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Elastic Potential energy is called the spring potential energy, which is the energy
stored in a spring (or elastic object) when the spring is stretched or compressed.
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Mechanical energy is the sum of potential and kinetic energies.
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Work is done when a force acts over a distance parallel to that force.
When work is done on an object, energy can change.
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Power is defined as energy used per second, or work done per second.
If a force acts at an angle to the displacement, break the force into components.
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The component perpendicular to the displacement does no work.
The component parallel to the displacement does work.
Calculating Net Work: Can calculate work done in two ways. So choose one way.
1. Determine the net force using a free-body diagram. Then multiply the component of the
net force that is parallel to the displacement by the displacement (eg. Fcosθ x d)
2. Determine the change in energy of the system. If there is a change in a type of energy,
work has been done.
Law of Conservation of Energy: Energy changes from one form to another, but is never
created or destroyed.
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If there is no friction, the total energy of a system remains the same.
If there is friction, the friction force does work on the system, and then the total
energy of the system will change (energy is not conserved)
Tip: Whenever the force on an object is changing, use energy conservation methods.
These are situations like curved roads, springs and pendulums.
Practice:
Suppose in the lab one group found that a spring has a spring
constant of k =1000 N/m . Construct a graphical representation of
force vs. displacement. (Hint: make the maximum displacement
0.25 m.)
1. Graphically determine the amount of energy stored while
stretching the spring described above from x = 0 to x = 10. cm.
2. Graphically determine the amount of energy stored while
stretching the spring described above from x = 15 to x = 25 cm.
3. The spring below has a spring constant of 10 N/m. If the block is pulled 0.30 m horizontally to the
right, and held motionless, what force does the spring exert on the block? Sketch a force diagram for
the mass as you hold it still. (Assume a frictionless surface.)
4. The spring below has a spring constant of 20 N/m. The μs between the box and the surface is 0.40.
a. The box is pushed to the right, then released. Draw a force diagram for the box above when the
spring is stretched, yet the box is stationary.
b. What is the maximum distance that the spring can be stretched from equilibrium before the box
begins to slide back?
5. A 60 kg student jumps from the 10 meter platform at a swimming complex into the pool below.
a. Determine her PEg at the top of the platform.
b. How much KE does she possess at impact? What is her velocity at impact?
c. Repeat steps a and b for a 75 kg diver.
d. If she jumped from a platform that was twice as high, how many times greater would be her
velocity at impact?
e. How much higher would the platform have to be in order for her velocity to be twice as great?
6. A spring whose spring constant is 850 N/m is compressed 0.40 m. What is the maximum speed it
can give to a 500 g ball?
7. If the spring in #6 were compressed twice as much, how many times greater would the velocity of
the ball be?
8. A 0.50 kg lab cart on a frictionless, horizontal surface is attached to a spring. The spring is
unstretched at position x = 0. The cart is released from rest at the position x = +0.25 m at time t=0.
a. Sketch a graph of the kinetic energy and also a graph of the potential energy of the cart as a
function of position x.
b. Sketch a graph of the total mechanical energy of the cart-spring system as a function of position x.
c. Sketch a graph of the speed of the cart-spring system as a function of position x.
d. Sketch a graph of the force applied by the spring on the cart as a function of position x.
e. Sketch a graph of the acceleration of the cart-spring system as a function of position x.