Resultant velocity is calculated using which two math functions

Physics Lab Report
s

PHET Lab C –Vectors & 1-D & 2-D STUDENT NAME: __________Jesssie Gomez_________

LAB FOR VECTORS AND 2-D MOTION

Lesson Plan for MATH-Vector Addition and PHYSICS-Two-Dimensional Motion Simulations (combined time 100 minutes)

LAB OBJECTIVES :

VECTORS

· Differentiate between scalar and vector quantities

· Graph addition and subtraction of vectors

· Multiplication and division of vectors by scalars

· Determine vector components using Pythagorean Theorem and trigonometric functions

· Calculate resultant vector for addition and subtractions

2-DIMENSIONAL MOTION

· Projectile Motion

· Identify velocity and displacement components of the parabolic function

· Calculate projectile motion problems using kinematic equations

BACKGROUND :

Students will review vector calculation, addition, subtraction, and scalar operation through the interaction with the vector addition simulation from the MATH catalog from PHET labs. To complement and review two-dimensional motion, students will work with the Physics simulations for 2-D motion and Projectile motion. As supplementary materials, students will be introduced to pre/post lab conclusion questions.

INTRODUCTION TO SIMULATIONS :

· For the Vector Addition simulation, go to the MATH menu as shown or go to: https://phet.colorado.edu/en/simulation/vector-addition

· For the 2-Dimensional Motion simulation, go to the PHYSICS menu as shown or go to: https://phet.colorado.edu/en/simulation/legacy/motion-2d

· For the Projectile Motion simulation, go to the PHYSICS menu as shown or go to: https://phet.colorado.edu/en/simulation/legacy/projectile-motion

STEP BY STEP INSTRUCTIONS :

Pre-Lab Assignments:

On your own: (Be sure to set your calculator in degree mode)

· After reading your textbook, complete the following pre-lecture problems and concept questions for vectors in 2-D motion.

1. In a paragraph describe whether or not the resultant vector of two opposite vectors will always involve the subtraction of vectors and what would be the resultant angle. Use a graphical representation to justify your answer.

2. Research and review significant figures concepts from your textbook to report all your responses with two significant figures.

3. After researching and reviewing accuracy and percent error concepts , describe how to determine these values in physics labs.

4. Show proper conversion (metric system) and calculations necessary in order to determine whether or not a person driving will have a resultant velocity of 19 mph if he/she first drives 11 mph east and then 8 mph north.

PhET Activities

Vector Addition – Use the Vector Introduction-Math simulation to complete the following:

1. In a paragraph and using your own words, explain what a vector representation is.

2. Before using the simulation, graph and predict which component of a resultant vector will be larger (the X or Y component) if you have a resultant vector of 62 Newtons at 59 degrees and justify your prediction. (Note, I am not asking you to calculate; I am asking you to estimate).

1. Define vector representation :

A vector is used in math when you want to represent both a magnitude and a direction. In physics we represent a vector by using an arrow.

2. Complete the following table BEFORE using any simulation.

Graph

Resultant

X-Component

Y-Component

Prediction Justification

Magnitude:

62 N

Direction:

59o NE

Magnitude:

___________

Direction:

___________

Magnitude:

Direction:

____________

Using the vector simulation, grab a vector arrow from the bucket and using the origin and 1st quadrant duplicate the above given problem (use resultant of 62 N @ 59o) and attach a screen shot of your model in the corresponding box of the next table.

Simulation Screen Shot

Resultant

X-Component

Y-Component

Were your predictions correct?

Magnitude:

62 N

Direction:

59o NE

Magnitude:

___________

Direction:

___________

Magnitude:

Direction:

____________

Why or why not?

· Complete the following table by using the same simulation. After clearing your screen, grab two new arrows from the bucket and create two different scenarios to demonstrate whether or not your answer to pre-lab assignment question 1. “ Do opposite vectors always result in subtraction and what happens to be the resultant angle? ” was correct.

Simulation Screen Shot

Vector 1:

Vector 2:

Resultant:

Scenario 1

Magnitude:

Direction:

Magnitude:

Direction:

Magnitude:

Direction:

Scenario 2

Magnitude:

Direction:

Magnitude:

Direction:

Magnitude:

Direction:

Projectile Motion Activity: Introduction to Projectile Motion

· Before using the Projectile Motion simulation, predict how varying initial conditions affect projectile trajectory (initial velocity, shooting angle, and horizontal and vertical displacement while ignoring air resistance). Use reasoning to explain these predictions.

Initial velocity:

Shooting angle:

Horizontal displacement/range:

Vertical displacement/maximum height:

Total traveled time:

· Complete the table below including screen shoots for the four different scenarios using a golf ball, concept definitions using your own words, changing the values as required, and describing the effects of those changes in regard to parabolic shape (longer/narrower/higher/lower), range (larger/shorter), angle (increased/decreased), and total time of traveled.

Simulation Screen Shot

Define Concept

Change Taking Place

Descriptions

Starting Scenario: ( insert screen shot)

Starting initial velocity of 12 m/s at an angle of 45o

No concept to define

None

Shape:

Range:

Angle: halved

Time:

Scenario 1

Define initial velocity:

Value of initial velocity:

Shape:

Range:

Angle: halved

Time:

Scenario 2

Define range

Value of range:

Shape:

Range:

Angle: halved

Time:

Scenario 3

Define maximum height

Value of maximum height

Shape:

Range:

Angle:

Time:

Scenario 4

Define time to reach maximum height

Value of tmax

Shape:

Range:

Angle:

Time:

· Describe why using the simulation is a good method for studying projectile motion.

· Predict the landing site of a ball launched horizontally (at ZERO angle) and vertically (at 90o angle).

Post-Lab Activities and Conclusions :

1. You take a walk in the park for 15 steps using a compass that points 25º north of east.

· How would you use the simulation to represent your path?

· Explain why the same representation works for illustrating this different scenario: You drive at 15 miles/hour using a compass that points 25º North of East.

· Write another scenario using different units that could also be represented with the same screen capture.

2. In the simulation, a vector is described by four measurements: |R|, Ө, Rx, and Ry. Put a vector in the work area and then investigate to make sense of what these four things represent. In your investigation, use a wide 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.

3. Suppose you are driving at 14 miles/hour with a compass reading of 35°north of east.

· Represent the vector using the simulation. How fast is your car traveling in the north direction?

How fast in the east direction? (include a screen shot)

4. To get to the sandwich shop, you left home and drove 6 miles south and then 10 miles west.

· If a bird flew from your house to the sandwich shop in a straight line, how far do you think the bird would fly? Use the simulation to check your reasoning.

· What direction should it fly from your house to get to the shop?

· Explain how you could use the simulation to answer these questions.

· Explain how you could use geometry equations to answer these questions.

5. Suppose you and a friend are test driving a new car. You drive out of the car dealership and go 10 miles east and then 8 miles south. Then your friend drives 8 miles west, and 6 miles north.

· If you had the dealer’s homing pigeon in the car, how far do you think it would have to fly to get back to the dealership? Use the simulation to test ideas.

· The distance that the bird has to fly represents the sum of the 4 displacement vectors. Use the simulation to test ideas you have about vector addition. After your tests, describe how you can use the simulation to add vectors.

6. A paper airplane is given a push so that it can fly 7m/s 35° north of east, but there is wind that also pushes it 8 m/s 15° north of east.

· Use the simulation to solve the problem. How fast can it go and in what direction will it travel?

· Think about your math tools and design a way to add vectors without the simulation.

· Check your design by adding several vectors mathematically and then checking your answers using the simulation.

*Sinθ = opposite leg/ hypotenuse Cosθ = adjacent leg/ hypotenuse Tanθ = opposite leg/ adjacent leg