Physics 116a02: Extra Hints for Assignment 5
Department of Physics and Astronomy, Vanderbilt University
Things to Think About for Assignment 5
Please read the problem statements carefully. There have been many
comments from the previous assignments about mis-reading the question, or the
format of the answer, and then losing credit.
- A Push or a Pull
- For parts G through N, you should be aware that friction acts in the two
situations which are being described. Friction is not discussed in the
text until Chapter 5, but we did talk about it in both lectures this week.
Also, be careful that you are clear in your mind about the right and the
left directions, and horizontal from vertical.
- For part M the problem asks you to think about what is happening
after the push force has stopped acting, and before the object
has stopped.
- Free Body Diagrams: Introduction (each problem part has a different
diagram on the left.)
- For part A and others: The problem statement uses the keyword smooth,
and defines that to indicate that there is no surface friction acting.
(For a real hockey puck on smooth ice, there would be some small amount of
friction, but it can be neglected in first order.) Similarly, the effects
of air resistance, or drag, are omitted even though they would contribute
in real life.
- For part B: The problem statement does not say that the horizontal
surface is smooth, so you should not assume that it is smooth. Also, be
sure to enter your answers in correct alphabetical order and without any
commas.
- For part C: There is a possibility of some confusion here. The free body
diagram which is shown on the right refers to part B problem. The answer to part C
refers to the new diagram on the left showing a block at rest on
an inclined plane.
- For part F: When you see the answer to part F, one of the forces is missing
a subscript which explains better what kind of force it is. Which one of the
forces is missing the subscript, and what should the subscript be?
- For part G: The block is no longer at rest but is sliding up the
inclined plane after having been given a push up the plane.
- For part H: In the diagram answering part H you will see that extra
(and different) subscript included. Could it be possible for the block to
be sliding up the plane at constant speed in reality? What about sliding down
the plane at constant speed?
- For part I: The inclined plane is now said to be smooth, which is
different from all the preceding parts.
- For part J: There is another new diagram. Does this look familiar to any
class demonstration?
- For part K: This is a rough horizontal table.
- Applying Newton's Second Law
- For part B: There is a special figure for this situation on the left. You
will likely want to refer back to the Intro figure before giving your answer
here. Don't worry about the relative lengths of the vectors depicted, but
concentrate on their directions.
- For part D: The x direction for block 2 is along the inclined
plane. There is no friction acting in this problem.
- For part E: The y direction for block 1 is vertical, and positive
in the upward direction.
- For part F: You have to think whether the ax acceleration for block 2 will be
positive or negative, and similarly whether the ay acceleration for block 1
will be a positive or a negative number according to the coordinate directions chosen
in the previous parts. (If I were teaching this problem in class, I would have
chosen the y direction for block 1 to be positive in the downward direction.)
It could help to think that block 1 is much more massive than block 2.
- For part G: The answer is slightly complicated. For testing the
correctness of your answer you could assume that the mass of block 2 is zero,
and see if the resulting expression is what you expect for the acceleration of block 1.
- Newton's First and Second Laws
- For part A: Terminal velocity is a constant velocity.
- For part B: In the answer option F, the acceleration could be up or down.
If answer option F is correct, in which direction is the acceleration?
- For part D: The problem statement does not say whether the 45 degree
deflection of the support string is along the long direction of the train
car, or possibly along the (shorter) width of the train car, or somewhere
in between these two directions. Does this omission make a difference in your
answer?
- For part G: The possibility that both cars have zero net force is not excluded by
the problem statement, nor the choice of answers.
- For part H: The forces can be acting in two dimensions, and in different
directions.
- For part I: The value mass is not given. What additional information would you
need to figure out the value of the mass? The answer feedback on this question
will have some pre-emptive statements about the preceding problems not being "tricky" or
"unfair", which may have been your reactions. However, I do agree that the
problems were not unfair, but sometimes subtle and did require that you read
carefully the information given.
- Free-body Diagrams
- For part A: The wheels on the piano allow you to ignore friction. In case
you did not realize it, all pianos have wheels for the reason of minimizing
friction when the pianos have to be moved. The piano is not sliding across
the floor (unless the wheels are stuck), but rolling across the floor.
- For part C: In the diagrams which I have drawn for the class lectures,
I have paid extra attention to the relative lengths of the force vectors too.
By knowing the relative lengths correctly, you get a better of idea of whether
there is a net force acting on the object of interest.
- For parts D and E: You need to look at the second diagram on the left.
- Newton's 3rd Law Discussed
- For part G: Anti-parallel has the same meaning as opposite in
direction.
- Tension in a Massless Rope
- For part A: You have to read carefully the problem statement on the left.
The three sections of the rope ("a", "b", and "c") are not actually demarked
definitively. You are told that point 1 is in section "a", while point 2 is
in section "b". If you want, you can assume that these two points are in
the middle of their respective sections, but your answers won't depend on
that assumption.
- For part D: Force magnitudes are always positive values, or zero,
but never negative values.
- For part F: There is no pulley involved in this problem. Also, I would
not have said "in the direction of the rope" since a rope doesn't point to the left
or to the right, for example. I would write the part D option as "along the
direction of the rope", as for a horizontal rope or for a vertical rope, which is the
way you should interpret option D.
- A Book on a Table
- For parts A through G: You must think carefully about each of Newton's 3
laws before answering these questions, especially the questions with only two
answer choices.
- Pulling Two Blocks
- For part B: This is a difficult question which tests your understanding
of Newton's Second Law. The blocks are being accelerated to the right.
- Exercise 4.3
- Exercise 4.8
- Exercise 4.11
- For part C: Assume that the same force is applied from 5 to 7 seconds,
after having not been applied between 2 and 5 seconds. You have to think
carefully of the characteristics of the motion during the whole time from 0 to 7 seconds.
- Exercise 4.24
- For part A: Again, remember that magnitudes of vectors are always positive
quantities, or zero.
- Exercise 4.38
- Exercise 4.54
- For part A: Unlike previous problems, the connecting rope in this problem
does have a mass. You can think that part of the force F must support the
total weight, and the other part is responsible for the acceleration upwards.
- For part C: It could be helpful for you to think about the rope as being two
masses of 2 kg each.
- Exercise 4.26
- For part A: Just because the problem asks for a plural "force vectors",
don't assume that there is more than one vector to be drawn.
- Exercise 4.60
- For part A: You will need to use calculus for this problem. Extra thought
questions: do the coefficients k1 and k2 have the same dimensions or the
same units? What are the dimensions or typical units of these two
coefficients? (The unit vectors are dimensionless.)
- Test Your Understanding of Newton's Second Law
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This page was last updated on January 30, 2008