1. Force Table Lab Vector Addition

2. Scale: 1 N = 20 cm Therefore: A = (0.392 N)(20 cm/N) = 7.84 cm B = (0.491 N)(20 cm/N) = 9.82 cm C = (0.294 N)(20 cm/N) = 5.88 cm Note: draw all vectors using arrows with a scaled length corresponding to the value of the vector, and starting from the origin (Point P). Add A to B graphically to determine the equilibrant vector R, which should be the same as C. Draw the equilibrant to R and measure the angle between R and C to determine error. P B = 9.82 cm A = 7.84 cm C = 5.88 cm θ ~ 10.5 ° R = 5.87 cm

3. Scale: 1 N = 20 cm Therefore: A = (0.392 N)(20 cm/N) = 7.84 cm B = (0.491 N)(20 cm/N) = 9.82 cm C = (0.294 N)(10 cm/N) = 5.88 cm Note: draw all vectors using arrows with a scaled length corresponding to the value of the vector, and starting from the origin (Point P). Draw an x and y axis so that one of the vectors lies along the axis. In this case it is vector A. Find the x and y components of the A and B vectors and add them together to determine R. P B = 9.82 cm A = 7.84 cm C = 5.88 cm x y

4. Find the components of B first: - Since there is no y-component, the x- component is the same as B. - B x = B = 0.491 N = 9.82 cm - B y = 0 Find the components of A using trigonometry. - A x = Acos θ - A x = (0.392 N)(cos 216.5°) = -0.315 N - A x = (-0.315N)(20 cm/N) = -6.30 cm - A y = Asin θ - A y = (0.392 N)(sin 216.5 °) = -0.233 N - A y = (-0.233 N)(20 cm/N) = -4.66 cm P x y BxBx ByBy 36.5 ° or 216.5 ° B x = -6.30 cm B y = -4.66 cm

5. P x y BxBx ByBy Add the x and y components of both the A and B vectors to get R x and R y. Then use the Pythagorean Theorem to find R. - R x = A x + B x = 6.30 cm – 9.82 cm - R x = 3.52 cm - R y = A y + B y = -4.66 cm + 0 cm - R y = -4.66 cm Solve for R: - R = √ R x 2 + R y 2 - R = √ (3.52 cm) 2 + (4.66 cm) 2 - R = 5.84 cm = (5.84 cm)/(20 cm/N) - R = 0.292 N RxRx RyRy R = 0.292 N

6. P x y Draw the equilibrant to R and compare to C. - From the previously determined value for R the estimate of error is 0.002 N, or 0.04 cm (~0.7%). - To determine the angle , use tan -1 (R y /R x ). You must then add 180 o to this value and compare to the angle for C in order to determine the angle . RxRx RyRy R = 0.292 N  ~ 10.5 °  Determining  :  = tan -1 (R y /R x )  = tan -1 (0.233N/0.176N) or  = tan -1 (4.66cm/3.52cm)  = 52.9 o