urgent , phys lab

Name:   Section   Date:   Pre  lab  Questions:   Answer these questions before coming to the lab and turn in your answers at the beginning of the lab to get credit. Turning this pre lab question sheet later would result in not getting any credit for the pre lab.

1. Using a ruler and a protractor draw a vector of 15 m/s oriented at 220o. Use a scale of 1 cm=5 m/s. Angles are measured counterclockwise from the positive x axes (0o) .

b) Clearly draw the components and measure them. (HINT: look in the lab manual if you don’t know how to draw them).

x-component= cm= m/s

y-component= cm= m/s

c) Calculate the x- and y- components using analytical method. Show your calculation to get credit.

x-component= m/s

y-component= m/s

d) Compare calculated and measured components. Discuss your finding.

2. The vector showed in the picture represents force in Newton. a) Using your ruler and protractor determine the magnitude and direction of the vector.

The scale is 1 cm= 1N. Angles are measured counterclockwise from the positive x axes (0o).

Magnitude= cm= N

Direction= o

b) Clearly draw the components of the vector and measure them. Record your answer.

x-component= cm= N

y-component= cm= N

c) With the values of magnitude and direction found at a), calculate components using analytical method. Show your calculation

x-component= N

y-component= N

d) Compare the results from b and c. Are the components equal, discuss your finding.

Name: Section: Date: Bring a cm ruler and a protractor for this lab.

Vectors and Applications

Objectives: To understand and practice adding vectors using tail to head method. To understand the components of vectors and how to analytical add them.

Materials: Protractor, ruler, US Map, calculator and individual handout provided by the instructor.

Overview: In this activity, you will use both the head-to-tail method and the analytical method of vector addition to determine the resultant displacement of a trip that have three individual “legs.”

Each student should receive from the instructor a handout

with the three vectors 𝑨, 𝑩, 𝑪 and a starting point. Record your vectors in the Table below. Starting point:

Vector A (km) Magnitude and direction

Vector B (km) Magnitude and direction

Vector C (km) Magnitude and direction

Part 1 Lab Procedure: Head-to-Tail Method to add vectors: Use only the ruler, protractor and the US Map at the end of the handout.

1. Use the scale provided by the US map legend provided at the end of this handout to convert the magnitude of the vectors given in km into cm. Record below

Vector A (cm) Vector B (cm) Vector C (cm)

2. On the US map find your starting point based on where the handout tells you to start.

3. Draw vector 𝑨   using your protractor at the starting point to determine the direction first (measure angles from the positive x axes going counterclockwise), then using your ruler measure the magnitude of the vector (length in cm).

4. From where your vector 𝑨   ends (do not go back to starting point), continue

with vector 𝑩 following the same procedure: with protractor find the direction of the vector and with ruler measure its length.

5. Repeat for vector 𝑪. This procedure shows you how you add three vectors (𝑨, 𝑩, 𝑪) in a head-to- tail fashion. To get credit include an arrowhead on each vector and label them clearly as 𝑨, 𝑩, 𝑪.

6. Connect your starting point to the ending point (where your last vector ends) with a line. This is the vector sum (resultant) of the three vectors also called total displacement vector. This resultant vector always points to the ending point, be careful how you draw the arrow and label it as 𝑅.

7. Using your protractor at the tail of the resultant vector (starting point) measure the direction of the resultant 𝑅.

8. Using your ruler measure the magnitude (length) of the resultant vector and convert it back to km. Magnitude of Resultant 𝑹= cm= km Direction of Resultant 𝑹=

Part II Lab Procedure: Analytical Method of Determining the Resultant: Now use ONLY a calculator and trigonometric functions to determine the

components of each vector in km.

Seeing the x-component: If you drop a line from the tip of the original vector straight down to the x-axis and draw a vector along the x-axis from the origin to where this line hits the x-axis, then this newly drawn vector is the x-component of the original vector. In the diagram the line that was dropped down is shown as a thin black line and the x-component is shown as a red vector:

Seeing the y-component: If you drop a line from the tip of the original vector straight down to the y-axis and draw a vector along the y-axis from the origin to where this line hits the y-axis, then this newly drawn vector is the y-component of the original vector. In the diagram the line that was dropped down is shown as a thin black line and the y-component is shown as a green vector:

Here is an example to help you understand how you draw and calculate the x- and y- components of a vector. The magnitude of vector 𝐹 is F=316 N and its direction is θ=350.

The x-component is called Fx: 𝐹! = 𝐹  𝑐𝑜𝑠  𝜃  and its y-component is called Fy: 𝐹! = 𝐹  𝑠𝑖𝑛  𝜃.Therefore: Fx= 361 N x cos 35o= 295.7 N and Fy= 361 N x sin 35o=207 N (calculator should be in degree mode! to calculate this).

35O

�⃗� = 316  𝑁

Fx

F y

x

y

Procedure to follow when adding vectors using component method:

1. Calculate the x- and y-components of each vector 𝐴(Ax, Ay), 𝐵( (Bx, By), 𝐶( (Cx, Cy). If you know magnitude  𝐹 and direction 𝜃 :

• the x-component of a vector 𝐹: the y-component of a vector 𝐹: 𝐹! = 𝐹  ×  𝑐𝑜𝑠  𝜃 𝐹! = 𝐹  ×  𝑠𝑖𝑛  𝜃

Record all components in table below.

2. Add the x-components of all the vectors to find the x-component of the resultant: Rx=Ax+Bx+Cx. Record in Table below.

3. Add the y-components of all the vectors to find the y-component of the resultant: Ry=Ay+By+Cy. Record in Table below.

Vector x- Component (km) y-Component (km)

𝐴

𝐵

𝐶

𝑅

4. Now that you have the x- and y-components of resultant vector, calculate the magnitude of the resultant vector using Pythagorean Theorem:

𝑅 = 𝑅!! + 𝑅!!

5. Calculate the direction:

𝜃 = tan!! 𝑅! 𝑅!

Magnitude of 𝑅= km

Direction of 𝑅=

6. Check to see if the direction matches the quadrant, if not adjust the angle accordingly.

7. Compare the magnitude of the resultant found when using the US Map (graphic method) with the analytical method by calculating a percent error.

Magnitude found while using US map is measured magnitude RM. Magnitude found while using analytical method is calculated magnitude RC.

8. % error for magnitude=|RM-RC|/RC x 100=

9. Compare the direction of resultant found when using the US Map (graphic method) with the analytical method by calculating a percent error.

Direction found while using US map is measured direction θM. Direction found while using analytical method is calculated direction θC.

% error for magnitude=|θM-θC|/θC x 100=

10. Using the results of the two methods of vector addition evaluate the effectiveness of the methods and the accuracy of your measurements.

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