PHYS 1001 Indiana University Purdue Week 3 Projectile Motion Project Ignore the discussion, only the other part PHYS 1001 – Week #3 – Summer 2020 Nonlinear

PHYS 1001 Indiana University Purdue Week 3 Projectile Motion Project Ignore the discussion, only the other part PHYS 1001 – Week #3 – Summer 2020
Nonlinear Motion
Context
Motion is not always constrained by a floor or a rolling track or a pulley system, as the systems
we have studied in weeks 1-3 have been. This week we will be studying two systems where the
motion of the object takes place in two dimensions, but the net force acts only along one
dimension and one system where the acceleration changes direction in a regular way. When
observing and analyzing these systems, you will need to use the tools we have developed over
the last three weeks: motion maps, vector addition, Newton’s Laws, and the conservation of
energy.
Materials:
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Something to toss from hand to hand: ball, balled-up sock, LEGO brick, etc.
Braded string from the lab kit
A block made of LEGO bricks
Laptop with LoggerPRO and camera for video capture and analysis
Objectives:
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Use motion maps to illustrate the trajectories of objects moving with non-linear motion.
Use force vector diagrams and Newton’s 2nd Law to evaluate the motion objects moving
with non-linear motion.
Use two mathematical approaches to determine the tension in the string for the conical
pendulum.
Part A: Projectile Motion
Anyone who has watched a ball game or watched the water in a fountain has witnessed the
ballistic motion of the ball in flight. The forces acting on the ball or water droplets while in
flight gives the trajectory its characteristic shape.
Figure 1. The jet of water from the foreground fountain clearly shows a roughly parabolic trajectory.
While a projectile is in flight, it experiences interactions with the Earth and with the air. Your
goal for this part of the experiment is to evaluate whether or not drag forces from air friction
have a noticeable effect on the motion of the projectile motion of a marble or of a ping-pong
ball undergoing projectile motion
1. Toss a marble or a ping-pong ball from hand to hand so that it moves approximately
equal distances horizontally and vertically.
2. Collect video showing the motion of the ball from the side so that you can see the arc of
the motion, making sure that a scale object is visible.
3. Create position versus time and velocity versus time graphs for the horizontal and
vertical motion of the ball.
4. Evaluate the motion of the ball using the graphs of the motion. What are the horizontal
and vertical accelerations of the ball? Show your work and explain your reasoning.
5. Draw an appropriate force diagram for the ball. Is the interaction between the ball and
the air small enough to be negligible? Explain your reasoning.
Part B: Forces & Acceleration for Planar & Conical
Pendulums
System B.1 – Planar Pendulum
Observation Experiment
Create a pendulum from a light piece of string or dental floss and a block made from your LEGO
bricks like the one shown in the Figure below. Make note of the block’s total mass.
Figure 2. A pendulum made from LEGO blocks and string, suspended from a closet rod.
Wrap the pendulum’s string around your finger and let it swing back and forth through an arc
that reaches its maximum height at about 45° from vertical. Do you feel any change in how the
string presses on your finger when the pendulum is at different points of the swing? Think
about why this could be. To help answer the question, work with your group members to
answer the following questions.
a. Consider different points along the arc, including the very bottom. Draw velocity
vectors at those points. What can you say about the lengths of the velocity vectors?
b. Use the velocity technique shown in Physics Tool Box 5.1 on page 122 of the Etkina
textbook to determine the direction of the acceleration of the pendulum bob at four
locations: at the top of the swing on the right; at some intermediate point when the
pendulum is moving down; at the bottom of the swing; at some point on the left before
the pendulum reaches the highest point.
c. What patterns do you notice? Does the acceleration of the pendulum bob always point
toward the center of the circle? If so, how do you know? If not, can you explain why it
does not? Explain why the acceleration points straight upward at the bottom of the
swing.
Test Your Ideas
Now that you have figured out how to determine the direction of the acceleration of the
pendulum bob at the bottom of its swing, use everything you have learned about circular
motion so far to make a prediction of the outcome of the following experiment:
d. An approximately 0.10 kg object hangs at rest from a string as shown below. The other
end of the string is attached to a spring scale calibrated to measure force. The string
pulls up on the ball exerting a ~1 N force and the string and ball in turn pull down on the
scale exerting a ~1 N force. The scale reads v ~1 N. The ball is then pulled to the side
and released so that the ball swings like a pendulum at the end of the string. Predict the
scale reading as the ball passes directly under the scale. Will it be more than, less than,
or equal to 9.8 N. Explain your reasoning.
Figure 3. The scale records the string tension which equals the weight of the ball when it hangs at rest.
e. Open the link below and watch the video of this system created by Brookes and Etkina
(http://www.islephysics.net/pt3/movies/Pendulum_New.mp4 ). Compare their results
to your predictions. Use force diagrams to show how the tension force magnitudes
shown on the scale work together with the gravitational interaction between the Earth
and the ball to give an acceleration consistent with the acceleration and velocity vector
diagrams you created above. Explain your reasoning.
System 2 – Conical Pendulums
The planar pendulum in System B.1 had an acceleration that changed during the motion. Many
motions, including those of the hunting cheetah shown below, have some combination of
change in speed and change in direction.
Figure 4. Acceleration arrows are placed along the trajectory graph of a cheetah’s successful hunt. It
starts at the origin, speeds up, and then chases its prey in a roughly oval path until the final pounce.1
Uniform circular motion is a special case of motion in two dimensions where the object moves
in a circular path at a constant speed. In the arcing motions of a planar pendulum, the direction
of the net force changes during the motion. As you can see in the video by Alom Shaha included
in the D2L folder for this week’s lab, there must be a force toward the center of the motion to
change the direction of the motion without causing the pendulum bob to speed up or slow
down in the process. Radial acceleration toward the center of the circular path is called
centripetal acceleration from the Latin centri ≡ center and petere ≡ seeking. The operational
definition of centripetal acceleration in physics is based on the parameters that affect the size
of the centripetal acceleration needed for the object to travel at a certain speed, v, around a
circle of radius, r. Then we use the circumference of the circle in our calculation of v.
v 2 ( 2 r )
4 2 r
= =
=
r
rT 2
T2
2
(1) acent
Where T is the period of the motion. The centripetal force, unlike the elastic force of a spring or
the tension force in a rope, is more of a committee title than the name of a single type of force.
The centripetal force is the sum of all the radial forces, with inward being the positive direction.
1
Wilson, A., Lowe, J., Roskilly, K. et al. Locomotion dynamics of hunting in wild cheetahs. Nature 498,
185–189 (2013). ( https://0-www-nature-com.libus.csd.mu.edu/articles/nature12295 )
(2) Fcent =  Fradial
The centripetal force and the centripetal acceleration are related to one another according to
Newton’s second law.
Figure 5. A mass travels in a horizontal circle at the end of a conical pendulum.
In a conical pendulum system, the bob at the end of the string moves in a horizontal circular
path while the string marks out a cone. Use the same pendulum as before, but this time swing
it in a motion as shown below. Your goal is to use video analysis and two mathematical
methods to determine the tension in the rope or the tangential velocity of the bob as it moves
around its circular path. Pick one of the two options.
a. Write a description in words of each of the methods you will use to determine your
chosen unknown. Draw a labeled sketch of your system to accompany a screen shot of
the pendulum’s motion. Include any relevant force diagrams and motion maps to
illustrate the motion.
b. Identify the physical quantities that you will measure than the quantities you will
calculate. List any assumptions that you make in your mathematical procedure. List
sources of experimental uncertainty and the ways to minimize them.
c. Then perform the experiment(s), record your results, calculate your uncertainties, and
compare your results. Discuss how the assumptions and experimental uncertainties
contribute to the discrepancy between the outcomes of the two mathematical
techniques.
Discussion Prompt – Week #3
Several students are discussing the motions studied in this week’s lab activity. Each of them
has something about their claim that is correct and something that needs refining. Evaluate the
pros and cons of the method in question. Then reply to one other person’s initial post and
reply to the commenter on your own post. Refer to your own method in your posts including
photos and/or force diagrams as relevant.
1. Winnifred (red) held the pendulum in her hand and filmed from above the support point of
the pendulum with the reference length on the floor.
2. Xavier (green) hung his pendulum from his closet rod and filmed with his phone on the
ground looking upward at the pendulum from below. He used LEGO block pendulum bob as
the reference length.
3. Yolanda (yellow) hung the pendulum from a shower-curtain rod and filmed a side-view of
the pendulum with her laptop camera. She used the length of the string as the reference
length.
Bonus Challenge:
Hold your cell phone in your outstretched hand with the Physics Toolbox Sensor Suite
accelerometer open and running. As much as you can, keep the phone flat so that one axis is
vertical and the two horizontal axes point radially and tangentially as you spin in a circle.
Determine your angular velocity from the acceleration values you record. Draft a friend or
family member to film you when you are spinning. If you get dizzy when you spin or cannot
perform this yourself for any other reason, draft your friend to spin while you film them. Show
your work and explain your reasoning. (4 pts)
Analysis Rubric:
Each of the criteria below will be evaluated on the following 4 pt scale. Maximum points will be
given if the work is clear, complete, and correct. No points will be awarded if no work was
submitted for the criterion or if the quantity and quality of the work was insufficient to be
evaluated. 1 point will be awarded if the student submitted work that started from incorrect
mathematical models, was self-contradictory, or was otherwise incorrect. 2-3 points awarded if
the work was partially or mostly correct, but there were errors or omissions in the work.
1. Data Acquisition & Graphical Representation, Part A.1-A.3: Be sure to identify your
tossed object and its mass. The mass of sports balls can be found online.
2. Evaluate graphs, Part A.4: Determine the horizontal and vertical components of the
acceleration. Show your work and explain your reasoning.
3. Force Diagrams, Part A.5: Evaluate whether air-resistance is negligible. Show your work
and explain your reasoning
4. Motion Map with Velocity Vectors, Part B.1.a: Make sure that the spacing of the points
and the length of the velocity arrows reflect the magnitude of the velocity.
5. Acceleration Vector Determination, Part B.1.b: Use the method described in the
textbook to determine the direction of the acceleration vectors at the moments
described.
6. Evaluate Motion Diagrams, Part B.1.c: Discuss the patterns seen relating acceleration
and the changes in motion of the planar pendulum
7. Make a Prediction, Part B.1.d: Make sure that you can explain your prediction based on
the work in Part B.1.a-B.1.c.
8. Evaluate Brookes & Etkina Video Compared to Parts B.1.a – B.1.d: Show how the
tension force and the gravitational force work together at different points in the motion.
9. Description of Mathematical & Experimental Strategy, Part B.2.a: Illustrate your
description with appropriate sketches, diagrams, etc.
10. Data Collection & Analysis, Part B.2.b: Submit appropriate data tables and sample
calculations. Use appropriate units and significant figures.
11. Compare and Evaluate the results, Part B.2.c: Do the two values agree to within
experimental uncertainty? Explain your reasoning.

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