Physics 116a02: Extra Hints for Assignment 6
Department of Physics and Astronomy, Vanderbilt University
Things to Think About for Assignment 6
- Contact Forces Introduced
- For part C: I don't like any of the answers to the question being posed
"..why the box accelerates down the board?". In fact, I think answer
C is at least as correct as the presumed right answer A. The correct
answer in my opinion is that Fg has exceeded the static friction maximum,
and thus Fg will be automatically larger than the kinetic friction.
Saying Fg is constant as in the nominal right answer A
might lead you to believe with Fg
does not change as the board is tilted to greater angles, which is
certainly false.
- For part D: This is an extremely tricky question. For example, you should
not assume that the car is going in a circle at constant speed, nor
should you assume that the road surface is frictionless. Finally, I would have
worded the last option answer as "If sufficient information is provided then
the normal could be found using ..." I am not a fan of tricky questions,
at the introductory course level, since they can give the impression that
Physics is a game of "gotcha".
- A Friction Experiment
- For all the parts, you have to look at each part's figure on the left,
and review the introductory figure, before giving your answer.
- For part A: Once the object starts moving, the frictional force
becomes kinetic friction only.
- For part B: Same hint as for part A.
- For part C: Although the statement of the problem says "assume the presence
of both static and kinetic friction", you should also realize that only one
type of friction is present for any particular value of Fx. This is not
a trick question.
- A Mass on a Turntable: Conceptual
- For part A: Again, you have to look at the special figure for part A.
- For part B: The questions about the speed of the particle are premature,
since we will not cover rotational motion until Chapter 9. You can assume
that the speed decreases linearly with radial distance, which you might have figured out on your own,
because the mass is moving in a smaller circumference distance in the same
amount of time as before. There still could be more than one correct answer
statement, however.
- Boat Statics
- For part A: No hints needed, except that the diagram is unnecessarily
complicated. The "E" and "F" capstan circles could have been omitted,
including the dashed lines from A to E and A to F.
- A Friction Experiment
- For part B: The physicist is continues to push the crate up the incline
but it is not moving. Hopefully, it did not take him too long to figure
out that he needed to ask for the help of another (smarter?) physicist, as he eventually did
in part C.
- For part C: Remember to think of all the forces acting on the crate.
- Kinetic Friction in a Block-and-Pulley System
- For part A: The answer is in terms of wA and wB,
or any other known quantities or numerical constants which you think are
needed.
- For part B: The supposed correct answer is |gwB/(wB + 2wA)|, using
the same kinetic coefficient as from part A. However,
I believe this problem statement is nonsense. If in part A the weight A
was moving at constant speed, that means that the weight B was just
heavy enough to overcome the kinetic friction that block A had with the table.
When the cat is on A, that means there is even more kinetic friction
expected. Hence, the blocks cannot move. Another way of seeing the mistake is
to realize that using the same kinetic coefficient of friction as in the answer
to part A, the kinetic friction force in part B would be 2wB, directed
to the left. Obviously, a wB vertically suspended weight could not cause
a horizontal movement to the right, and similarly friction cannot cause an acceleration to the left.
- The Normal Force
- Two Cars on a Curving Road
- For part A: You can assume that the road is horizontal. There is also a
poor wording "both cars need to maintain a net force F". This should have been
written "both cars have the same net force F acting on them" (and you might ask
yourself along what direction is this net force?). The "need to
maintain" might have you thinking that the cars were approaching the limit
of the frictional force, which is not the point of this problem.
- For part B: Continue to assume a horizontal road.
- Two Blocks and Two Pulleys
- For part C: Double pulley systems require some extra thought regarding
how much distance m2 will move in the same amount of time that
m1 moves. Try to visualize what happens when m1 moves down a
vertical distance s. Does m2 also move the same horizontal distance s in this
arrangement?
- For part E: If you managed to work through all five parts of this problem with correct
answers on the first try, you have done very well.
- Two Masses, a Pulley, and an Inclined Plane
- For part A: You are asked to compute a ratio of masses, and any ratio
of two similar physical quantities is dimensionless. So make sure that any answer
that you submit is also dimensionless. This is a tough problem, with 7 hints available.
- Circular Motion Ranking Task
- For part A: A somewhat strange setup since one normally thinks of
satellites in space orbiting around the Earth because of the gravitational
force of the Earth. In this problem, the satellites are apparently
tethered to the space station in the center of their orbits. The tension in
these tethers provides the needed centripetal force, since gravity is not a factor.
One can assume that there has been some propulsion system on each satellite which
has given them the speeds v as listed at the distances L listed.
The "period" (usually given the symbol T) of the motion is the time it takes to complete one orbit. We will
study such cyclical (oscillatory) motion more deeply in Chapter 13.
- Normal Force and Centripetal Force Ranking Test
- Normal and Frictional Forces Ranking Test
- Exercise 5.14
- Exercise 5.5
- Exercise 5.44
- No extra hints needed, but a complicated answer in part B.
- Testing Your Understanding 5.3: Frictional Forces
- Testing Your Understanding 5.4: Dynamics of Circular Motion
- Problem 5.80: Traffic Court
- For Part B: Apparently a one decimal place answer is required.
- Problem 5.88
- For Part A: No extra hints needed. What do you think will happen if
block C is bigger than the correct answer? In that case will block B have any acceleration
at all, while it is still in contact with block A? Could you find an expression
for how much time it would take until block B was no longer in contact with
block C, assuming block B was originally in the middle of block C and you knew the width of block C?
- Problem 5.99: The Monkey and the Bananas (not really a good question, but
a thought-provoking one)
- For part A: You should assume that the weight of the monkey and the weight
of the bananas are the same. The monkey and the bananas are originally at rest,
which can only be possible if their weights are the same. Then the monkey
starts climbing the rope. What happens?
- For part B: If you tried to solve this problem thinking about mechanical
(gravitational) potential energy which we have not yet discussed anyway,
you would get the wrong answer. The monkey
is making use of stored chemical potential energy, just the way you do when
you move your muscles. You have to think of the problem in terms of the forces
and their effects on the two masses (monkey and bananas).
- For part D: The answer to this problem is much easier to understand
after you learn about conversation of mechanical energy.
- Problem 5.110: Ferris Wheel
- If you have never ridden on a Ferris Wheel, you should realize that
the seat in which the rider sits is always horizontal, and the rider is always
sitting upright. There could be a (horizontal) force of friction between
the seat and the rider. Assume that the Ferris Wheel is continuously in
motion when you answer these questions.
- Problem 5.114
- No extra hints needed. This problem is very much like the class
demonstration of swinging a cork in a horizontal circle where the cork
was connected by a string to vertically suspended tennis ball.
- Problem 5.119: Mass inside a rotating cone (very complicated expressions
for the solutions)
- For part A and part B: This problem is like the car on a banked highway curve,
except that there is static friction acting up or down the cone. As with the
car example, you should
draw the free body diagrams using a vertical and a horizontal coordinate
system, since the motion of the mass is in the horizontal direction. The
normal force from the cone and the friction force will each have components
in both the vertical and the horizontal directions.
- Problem 5.121: Mass on an accelerating inclined plane (difficult problem,
but a simple answer)
- For part A: There is no friction acting between the inclined plane
("wedge" of mass M) and the mass m on the wedge. You should draw
the free body diagram using a horizontal and vertical coordinate system.
The condition that the mass m remains at constant height is equivalent
to the dual conditions that the acceleration of m in the vertical y direction is
zero, and that the acceleration in the horizontal x direction is that
which you would get because the applied horizontal force F is acting on
a combined mass M+m.
- Problem 5.7: The Streets of San Francisco (the name of an old TV series with
the now older Michael Douglas as the young impetuous co-star)
- Problem 5.18: Row boats towed on an iced-over lake.
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This page was last updated on February 8, 2008