FA19_PHY_251_LabManual.pdf
Fall 2019 PHY-251 Lab Manual Page 17 of 56
Lab 3: Vector Simulation Exercise (Handout from Prof. Field – Edited by Prof. Ciocan)
Vector Simulation Exercise
In class, we’ve discussed the use of vectors to represent physical quantities as well as the use of
mathematical operations of vector addition, subtraction and multiplication by scalars. We have also learned
how vectors can be resolved by components. In this lab, you will work individually on a laptop and use
simulation software to manipulate vectors and gain a clearer understanding of the use of vectors and their
math operations with vectors.
OBJECTIVES:
- Understand and explain the use of vectors to represent physical quantities.
- Convert between the angular form of vectors and the component form.
- Add and subtract vectors graphically and by components.
MATERIALS
* Personal computer with internet access
PROCEDURE
Logon and Setup – Gain access to and set up the simulation software.
1. Go to:
https:
phet.colorado.edu/sims/vector-addition/vector-addition_en.html
2. A screen similar to the one shown below will appear:
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3. Check the Show grid box by clicking on it.
4. Click and drag a vector from the bucket of a
ows and place it anywhere on the screen.
5. Your screen should now look similar to the one below:
Practice – Gain familiarity with the operation of the simulation software.
1. Click on the vector in the grid space. Numbers should show up in the four rectangular boxes at the top
of the screen.
2. Note that you can change the location of the vector by clicking and dragging the shaft of the vector.
Try it.
3. Note that you can change the length and direction of the vector by clicking and dragging the pointed
end (tip) of the vector. Try it.
4. In this simulation, a vector is described by four measurements: R , θ , xR , and yR . Investigate what
these four things represent. In your investigation, use a variety of vector measurements and all three
styles of Component Displays. Then, describe in your own words what the measurements represent
and what “component” means.
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Exercises – Use the simulation software to explore the following scenarios and answer the questions.
Give two solutions for each exercise as follows:
Solution A – using the resolving or adding vectors by components as studied in the lecture part of this
course and including all necessary sketches and calculations;
Solution B – using the simulation and including all necessary screen shots and explanations.
1. Suppose you are driving 12.2 miles/hour with a compass reading of 35° (measured from the +x axis.
How fast is your car traveling in the y direction? How fast is your car traveling in the x direction?
Solution A Solution B
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2. Clear the grid space of all vectors by clicking on the red Clear All button. Then place two vectors
on the grid space and adjust them so they have different directions and magnitudes from one another.
Move one of the vectors so that its tail just touches the tip of the other vector. Your screen should now
look similar to the one below:
To get the resultant vector, check the Show Sum box by clicking on it. Move the green sum vector so that
the tail touches the tail of your first vector. This is an illustration of how triangle rule for vector addition
works.
Now change the magnitude and direction of the second vector by clicking and dragging its tip. Describe
your observations of the resultant vector’s behavior.
Solution A Solution B
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3. To get to the sandwich shop, you left home and drove 6 miles in the –y direction and then 10 miles in
the –x direction.
a.) If a bird flew from your house to the sandwich shop in a straight line, how far would the bird fly?
Solution A Solution B
.) What direction should the bird fly from your house to get to the shop?
Solution A Solution B
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4. Suppose you and a friend are test driving a new car. You drive out of the car dealership and go 10 km
in the +x direction, and then 8 km in the –y direction. Then, your friend drives 8 km in the –x
direction, and 6 km in the +y direction. If you had the dealer’s homing pigeon in the car, how far
would it have to fly to get back to the dealership?
Note: The distance that the bird has to fly represents the magnitude of the vector sum of the 4
displacement vectors.
Solution A Solution B
5. You go for a walk and take 20 steps in the +y direction. Use the simulation to represent your path.
Next, you turn left and walk 10 steps in the –x direction. How far from where you started did you end
up?
Solution A Solution B
Hint: Add the two vectors using the “sum”
utton.
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6. For the purposes of this problem, assume that the +y axis points north, the +x axis points east, the –y
axis points south, and the –x axis points west. You are flying a hang glider at 14.1 mph in the northeast
direction (45°). Then, the wind starts blowing at 4 mph from the north.
a.) What speed and direction (relative to the Earth) are you actually flying?
Solution A Solution B
.) The wind increases to 8 mph from the north. Now what is your actual speed and direction? If
your destination is to the northeast (45°), how would you change your direction (assuming you
can’t increase your airspeed) so you might make it there?
Solution A Solution B
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QUESTIONS
1. Which of the following are vector quantities and which are scalars: mass, weight, velocity, speed,
force, friction, displacement, length, time, acceleration, temperature?
2. In this simulation, you have worked with two-dimensional vectors. Do three-dimensional vectors
exist? How would you add such vectors graphically? How would you add such vectors by
components?