Vector Addition and Subtraction

Vector Addition and Subtraction Report

Your report must include the following: (notice this report is different than usual). You only need to type the cover page. Everything else is handwritten. Start each part in a separate page and include the headers for each section.

0.  Cover page (typed) / 5 points

1.  Step 1: Mass and Scale Conversion / 20 points

a.  Show one calculation of how to convert the masses from grams to weight in Newtons.

b.  List the answers for the other two masses.

c.  Show one calculation of the graphical scale conversion.

d.  List the answers for the other two vectors

2.  Step 2: Graphical Representation / 24 points

a.  Show the Graphical construction to scale of the sum A + B + C.

b.  Include the scale use to graph. Label vectors and angles

c.  List the value of the resultant in Newtons.

d.  List the angle it makes with the positive X-axis

3.  Step 3: Component Method / 24 points

a.  Use the component method to calculate R = A + B + C. Show all the calculation steps.

b.  Calculate the angle it makes with the positive X-axis.

c.  List the value of R in Newtons.

d.  List the angle it makes with the positive X axis.

4.  Step 4 : Percent Difference / 15 points

a.  Calculate the percent difference between the values in step 2 and step 3 for the resultant vector.

b.  Calculate the percent difference between the values in step 2 and step 3 for the angle.

5.  Step 5: Equilibrium Force: / 12 points

a.  Calculate the magnitude (in Newtons) and direction of vector E; such that,
A + B + C + E = 0

b.  Record all four values in grams that you set up in the force table.

c.  Record all four values of the angles that you set up in the force table.

6.  Total: / 100 points


Things to consider for this experiment

Step 1:

1.  To convert the mass from grams to a weight in Newtons, you must first convert the mass to kilograms and then multiply by g= 9.81 m/sec2.
Weight = mass * gravity

2.  You are converting your vector values from Newtons to cm values to graph them.

3.  The scale you are using is 3.50 cm = 1 Newton.

Step 2:

1.  Draw your vectors neatly and measure your angles carefully.

2.  You will read the value of R in cm and convert it back to Newtons.

3.  Measure the direction that R makes with the +X-axis in degrees.

Step 3:

  1. All vectors must be in Newtons when performing all calculations.

Step 4:

1.  You are comparing the values of R in step 2 and step 3. Remember the magnitudes must be in Newtons and the directions in degrees.

2.  You are calculating a percent difference. Refer to the previous handout for questions.

Step 5:

1.  Use the average value of R and θ to calculate E (the equilibrant).

2.  Do not forget to record the values of all four masses in grams (include the mass of the hanger) and all four angles in degrees from the force table.

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