Physical Sciences 2
September 20 – 27
Physical Sciences 2: Assignment for September 20 – 27
Homework #3: Forces and Motion
Due Tuesday, September 27, at 9:30AM
This assignment must be turned in by 9:30AM on Tuesday, September 27. Late homework will not be
accepted. Please write your answers to these questions on a separate sheet of paper with your name and
your section TF’s name written at the top. Turn in your homework to the basket in the front of lecture
with your section TF’s name.
You are encouraged to work with your classmates on these assignments, but please write the names of
all your study group members on your homework.
After completing this homework, you should…
• Be able to identify any constraints placed on acceleration in a given scenario
• Be able to identify the forces acting on an object (gravity, normal, tension, etc.)
• Be able to draw and label a free-body diagram
• Be able to apply Newton’s second law in a variety of situations to calculate unknown quantities
• Understand the difference between static friction and kinetic friction, and when to use each
• Understand the difference between viscous drag and pressure drag, and when to use each
• Be able to calculate the terminal velocity of an object
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Here are summaries of this lecture’s important concepts to help you complete this homework:
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0. Reflections on Last Assignment (1 pt)
Pick one question from Homework 2 that you found particularly difficult and:
a) describe the errors that you made
b) ways to ensure that you have learned from your mistakes so that you won’t have the same
trouble with such a question in the future
1. Iris and Javier (1 pt) Iris and Javier are playing on a playground rather than studying for their
physics exam…
Iris:
It’s your turn to sit on the merry-go-round, Javier!
Javier:
Iris, I see you haven’t been holding on as you sit on the merry-go-round. Well, I can do
that too – and I won’t slide off, as you just did. You see, since I’m heavier, the force of
static friction will be greater for me than it was for you. So, pfffft.
Iris:
Actually, Javy, you might want to check your physics notes again…
What’s wrong with Javier’s argument? Support your answer with a clear diagram and a derivation.
2. Forces and Constant Velocities (1 pt)
A rope pulls a box, as is shown in the picture. The
rope makes an angle θ with the horizontal and there
is friction present between the box and the surface.
The rope pulls the box at a constant velocity.
For which of the following velocities is the pulling force the largest? Your answer may contain some,
all, or none of these. Justify your answer.
i.
v = 0 m/s
ii.
v = 1 m/s
iii.
v = 10 m/s
iv.
v = 100 m/s
3. Rats! (1 pt) Coal miners often find mice in deep mines but rarely find rats; let’s see if we can figure
out why. A mouse is roughly 5 cm long by 2 cm wide and has a mass of 30 g; a rat is roughly 20 cm
long by 5 cm wide and has a mass of 500 g. Assume that both have a drag coefficient CD ≈ 0.3.
a) Estimate the terminal falling speeds reached by a mouse and a rat, respectively.
b) Assume that mine shafts are deep enough that both the mouse and the rat reach terminal velocity
before hitting the bottom. Estimate the magnitude of the maximum force required to stop both the
rat and the mouse when they hit the bottom. (Hint: Over what distance will the center of mass travel
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between the beginning of the collision and when the animal is at rest? What is the acceleration
required to bring the animal to rest over this distance?)
c) Bones will break if they are subjected to a compressional force per unit area of more than about
1.5 × 108 N/m2. A mouse may have leg bones about 1.5 mm in diameter; for a rat, they might be
about twice as thick. Using your estimates from part b), determine if either the mouse or the rat (or
both) will suffer broken legs. Is your answer consistent with the observations of the coal miners?
Explain.
4. Post-lab Assignment for Lab 2 (2 pts)
Last week in lab, you investigated conservation of momentum in the Gauss Gun system. Some groups
indicated that momentum was conserved, or close to it, while some groups indicated that momentum
was not conserved. The vast majority of these found that there was a change in momentum in the same
direction. (To remind yourself what your own result was, go to the “Laboratory” section of the course
website.)
Let’s see if we can understand why this happened. First, we’ll review our definitions:
In the initial state, ball 1 is rolling towards the magnet with some initial x-velocity v1i,x just before the
collision. We took the final state to be the time of the first video frame after the collision (not the time of
the collision itself). In the final state, the recoiling 1-M-2 system has a (negative) x-velocity v1f,x , and the
outgoing ball has a (large positive) x-velocity v3f,x .
a) The majority of groups observed that the final state had a larger x-component of total momentum
than the initial state, i.e. pf,x − pi,x > 0 . What can you conclude about the net external force on the
system during the time between the initial (just before collision) and final (first video frame after
collision) states? Draw the free-body diagram for the system during this time. What single force do
you think is mostly responsible?
b) Below is a graph taken from a Logger Pro video analysis, showing the incoming motion of ball 1
(blue) and the recoil of 1-M-2 (green), with the appropriate linear and quadratic fits displayed. Using
this graph, calculate µk , the coefficient of kinetic friction between 1-M-2 and the track. (Don’t
worry about uncertainty.)
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c) Recall that for a non-isolated system, the change in the system’s total momentum during some time
is equal to the total external impulse on the system during that time. We can’t calculate the total
impulse, because we don’t know how much time elapsed between the collision and the final state—
but we can put an upper bound on it, because we know that the time was at most one video frame
(33 milliseconds). For the experiment graphed above, calculate the maximum possible x-impulse
Δpx due to kinetic friction. You may need to know the masses: the mass of one ball was 8.36 g,
and the mass of 1-M-2 together was 22.76 g. The results of the experiment at the time were
pi,x = ( 268 ± 8 ) g ⋅ cm/s , and pf,x = ( 380 ± 40 ) g ⋅ cm/s . Could kinetic friction alone be enough to
account for the observed change in momentum?
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5. Putting Everything Together (Exam-Type Question): Newton’s Second Law Practice (2 pts)
Question from Tutorials in Introductory Physics
The table below provides information about the motion of a box in four different situations. In each
case, the information given about the motion is in one of the following forms: (1) the algebraic form of
Newton’s second law, (2) the free-body diagram for the box, or (3) a written description and picture of
the physical situation. In each case, complete the table by filling in the information that has been
omitted. Case 1 has been done as an example.
(All symbols in the equations represent positive quantities. In each case, use a coordinate system for
which +x is to the right an +y is toward the top of the page.)
KEY: B – box; C – small container; H – hand; S – surface; E – Earth; R, R1, R2 – massless ropes
a.
b
.
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c.
d
.
6. Putting Everything Together (Exam-Type Question): Don’t
look down! (2 pts)
Mountain goats (Oreamnos americanus) can climb steep inclines;
their hooves are designed to provide good traction against rock.
The image at right shows a mountain goat adult and kid on very
steep cliff in the Rocky Mountains in North America.
a) If a mountain goat with m = 90 kg is standing still on a
mountain with a θ = 60° incline (from the horizontal), what is
the minimum coefficient of static friction required between its
hooves and the rock?
To escape a predator, the mountain goat accelerates (with constant
acceleration) from rest to a velocity of 3 m/s directly up the incline
over a duration of 0.1 second.
b) Which force is responsible for accelerating the goat up the
incline: static friction or kinetic friction? Explain your answer.
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