B) I Ran Two Miles Due North Along the Lake. ______

Name______Date______

DISCOVERY LAB: VECTORS

1. For the following questions, which of the following statements involve vector quantities, and which involve scalar quantities?

a) I ran two miles at the lake. ______

b) I ran two miles due north along the lake. ______

c) The plane flew at a speed of 90 knots on a heading of 600 east of north. ______

d) The car was traveling at 60 mph.______

e) The temperature was minus 20 degrees. ______

f) The cart moved 20 meters in the negative x direction. ______

2. Vector A points due west, while vector B points due south. They both have a magnitude of 4.0 cm. Using a ruler,

Draw the graphical addition of A + 2B to scale. Label A, 2B, (A + 2B).

Draw the graphical subtraction, (A – B) to scale. Label A, B, A - B.

Measure the length of each vector to 1 decimal place:

A + 2B ______A – B ______

1 3. Vectors A and B are shown in the drawing below. Vector R (not shown) is the resultant vector where R = A + B. Indicate the signs (negative or positive) of the following scalar components:

Ax ____Ay ____Bx ____ By ____ Rx ____ Ry, ____

Exercises 4-6: Draw and label x- and y- components of the vector shown:

Exercises 7-9: Draw and label x- and y- components of the vector and determine their numerical values (including sign!):

2 10. A common objective in physics is to calculate the components of the gravity vector parallel and perpendicular to a hill or incline. The vector F points in the “true vertical” direction (represented by the long end of the paper). The axes are tilted so that the x axis represents the hill’s orientation with respect to horizontal. a. Draw the F vector on the diagram of tilted coordinate axes below (F must remain true vertical at all times): b. Draw the components FX and FY on the diagram: c. Calculate the numerical value and sign of FX and FY:

FX = ______

FY = ______

Exercises 11-16: Draw and label the vector with these components. Write the magnitude of the vector below, along with the appropriate acute angle.

Ax = -3, Ay = 2 Bx = -3, By = -1 Cx = -2, Cy = 0 θ = ______θ = ______* θ = ______

* not acute in this case!

3 Ax = -1, Ay = 2 Bx = 0, By = -2 Cx = 3, Cy = -2

A = ______B = ______C = ______

θ = ______θ = ______θ = ______

Exercises 17-19: In each case, the vector A is 5 units long and is directed 0 30 above true horizontal. Determine the components Ax and Ay for the three coordinate systems shown below. Show your work below the figure.

Exercises 20-22 use graphical representation of vector addition. For each force, determine the x and y components by counting the number of squares to the nearest half. Include the appropriate “+” and “-“signs. Then, add the total number x and y squares from all the forces and draw the net force vector on the graph provided.

4 EXAMPLE x y

F1 (N) 0 2

F2 (N) -2.5 0

F3 (N) 0 -3

F4 (N) 3.5 -3.5

Fnet (N) 1 -4.5

#20 x y

F1 (N)

F2 (N)

F3 (N)

F4 (N)

Fnet (N)

#21 x y

F1 (N)

F2 (N)

F3 (N)

F4 (N)

Fnet (N)

#22 x y

F1 (N)

5 F2 (N)

F3 (N)

F4 (N)

Fnet (N)

Exercises 23-25 review the addition of vectors (in this case force vectors) using the mathematical procedure of vector addition. The procedure for all of these problems is shown below.

1. Enter the vector components in the table for each force vector. Put in the appropriate “+” and “ – ” signs based on quadrant.

2. Add components in the last row of the table.

3. Find the magnitude and acute angle above/below positive/negative x axis and enter it below the table.

Draw the net force vector on the graph provided.

EXAMPLE x component y component

o o F1 (N) 40 cos 45 40 sin 45 28.3 28.3

F2 (N) 0 30

o o F3 (N) -50 cos 30 -50 sin 30 -43.3 -25

Fnet (N) -15 33.3

o Fnet = 36.5 N Θ = 66 above –x axis

6 #23 x y component component

F1 (N)

F2 (N)

F3 (N)

Fnet (N)

Fnet = Θ =

F1 (N)

F2 (N)

F3 (N)

Fnet (N)

Fnet =

#25 x component

F1 (N)

F2 (N)

F3 (N)

Fnet (N)

Fnet = Θ =