Physics 116a02: Extra Hints for Assignment 8
Department of Physics and Astronomy, Vanderbilt University
Things to Think About for Assignment 8
- Introduction to Potential Energy
- For part E: Assume that only conservative forces are acting.
Non-conservative forces, such as friction, do not have a potential
energy associated with them. Only conservative forces have
an associated potential energy. There can be systems, studied later,
which have both a conservative and a non-conservative force acting,
such as gravity and friction.
- Where is the Energy?
- For part B: The original setup of the problem essentially said that
the height of the plane is h. Can you see where that was implied?
- For part D: Algebraic signs are important in computing energy changes
(as well as for momentum changes in the next chapter's work).
- For parts E and part H: In the answer options which contain the Wnc term
(work done by non-conservative forces), you should assume that this term
is not zero. Otherwise, there are effectively duplicated answer choices.
- For part H: Slightly tricky, in my opinion. If hi and hf
are identical, then the program would say that you don't need those terms
in the equation. A better way of writing this question, and also for part E,
is "What is the simplest equation which describes the motion ..."
- Loop-the-Loop
- If this problem doesn't look familiar to you, then you need to come to
class more often.
- Shooting a Block up an Incline
- For part A: The answer is quite complicated. This is a hard problem which
tests your complete understanding of kinematic equations and energy principles.
You can assume that the spring is massless, and does not acquire any kinetic energy.
- Stretching a Spring
- For part C: The wording may be confusing. Instead of "the same amount of
energy is required to stretch both springs", I would say "the same amount of
energy is used to stretch both springs". Then in the answers Iwould replace "must
stretch" with "will stretch".
- Exercise 7.4: Diving into Water
- For part C: I don't know how it is possible to "jump downward" at a given speed, but the
question can be answered in any case.
- Exercise 7.12: Tarzan and Jane
- Exercise 7.38: Intepreting a potential energy graph U(x)
- For part A: We discussed in class that F(x) = -dU/dx. So if
the left side is zero, what does this tell you about the value of
the derivative on the right side of this equation?
- For parts B and C: You have to read pages 235 and 236 in the text.
You can imagine that the U(x) graph shown represents a
track with hills and valleys
on which a marble is placed. At what points on the track will
the potential energy be a minimum relative to nearby points (stable
equilibrium)? At what points on the track will the potential energy
be a maximum with respect to nearby points (unstable equilibrium)?
Mathematically, stable equilibrium position points for U(x) are where dU/dx = 0,
and the second derivative d2U/dx2 is positive.
Mathematically, unstable equilibrium position points for U(x) are where dU/dx = 0,
and the second derivative d2U/dx2 is negative.
- Exercise 7.42: Compressing a Spring
- Exercise 7.48: Up and Down the Hill
- For part B: In class we once talked about the angle of repose
for an inclined plane, and how one can determine the coefficient of static
friction for the surface of the inclined plane by knowing that angle.
- For part C: How does your speed answer here compare to the original 15 m/s
which the block had: bigger, the same, or smaller? If different, do you
understand why it is different?
- Exercise 7.63: Skiing Off a Snow Sphere
- This problem is somewhat related to the vertical loop problem. You have to
think of normal forces and weight components, as well as energy conservation.
- Exercise 7.75: Doing Work on a Mass Attached to a Spring
- Test Your Understanding 7.1: Gravitational Potential Energy
- Exercise 7.8: Crate Sliding on a Ramp
- For part C: Enter in one or two sentences which I will check.
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This page was last updated on February 15, 2008