Worksheet
Potential Energy Functions
Refer to the following information for the next fifteen questions.
A particle of mass 0.5 kg obeys the potential energy function
U(x) = 2(x - 1) - (x - 2)
^{3}
where x is measured in meters and U in joules. A graph of this function is given below.
What is the value of U(0)?
What are the values of x
_{1}
and x
_{2}
?
How much potential energy does the particle have at position x
_{1}
?
If the object was initially released from rest, how fast is it moving as it passes through position x
_{1}
?
How much potential energy does the mass have at x
_{2}
?
How fast is it moving through position x
_{2}
?
Which position, x
_{1}
or x
_{2}
, is a position of stable equilibrium?
How fast is the particle moving when its potential energy, U(x) = 0?
If x
_{3}
= ½x
_{1}
, then how fast is the particle moving as it passes through position x
_{3}
?
Sketch the graph of the particle's acceleration as a function of x. Indicate positions x
_{1}
and x
_{2}
on your graph. Describe your graph in the area provided.
At what value of x does the particle experience it greatest negative acceleration?
What is the value of its potential energy at this position?
How much kinetic energy does it have at this position?
What force is being exerted upon it at this position?
What is the value of its acceleration at this position?
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