Lab 5

Analysis of Vector Addition Lab Online Tables 1 Vector | ⃑ V | θ V x V y ⃑ a 18.0 33.7 15.0 10.0 ⃑ b 25.1 175.4 -25.0 2.0 ⃑ c 15.6 129.8 -10.0 12.0 ⃑ E 15.6 50.2 10.0 -12.0 Complete Table 1 with the values of the Equilibrant vector. (15 points) E = 180 – 129.8 = 50.2 = 50.2 1. Using trig and the properties of vectors show that for each vector the given polar coordinates are equal to the component coordinates. Show work for credit. (10 points) Given ( r ,θ ) = ¿ Ax = 18(cos(33.7) = 14.98 = 15.0 Ay = 18(sin(33.7) = 9.99 = 10.0 Bx = 25.1(cos(175.4) = -25.0 By = 25.1(sin(175.4) = 2.0 Cx = 15.6(cos(129.8) = -9.99 = -10.0 Cy = 15.6(sin(129.8) = 11.99 = 12.0 Ex = - Cx = -(-10.0) = +10.0 Ey = -Cy = -(12.0) = -12.0 2. Show that ⃑ a + ⃑ b = ⃑ c . Show work. (10 points) Ax + bx = cx  15.0 + -25.0 = -10 Ay +By = Cy  10.0 + 2.0 = 12 Tables 2 Vector | ⃑ V | θ V x V y ⃑ a 11.2 153.4 -10.0 5.0 ⃑ b 31.6 -18.4 30.0 -10.0 1

⃑ c 20.6 -14.0 20.0 -5.0 ⃑ E 20.6 166 -20.0 5.0 Complete Table 1 with the values of the Equilibrant vector (15) E = 180 + -14.0 = 166 3. Using trig and the properties of vectors, show that for each vector the given polar coordinates are equal to the component coordinates. Show work for credit. (10 points) Ax = 11.2(cos(153.4) = -10.0 Ay = 11.2(sin(153.4) = 5.0 Bx = 31.6(cos(341.6) = -29.98 = 30.0 By = 31.6(sin(341.6) = -9.97 = -10.0 Cx = 20.6(cos(346) = 19.99 = 20.0 Cy = 20.6(sin(346) = -4.98 = 5.0 Ex = - Cx = -(-5.0) = +5.0 Ey = -Cy = -(20.0) = -20.0 4. Show that ⃑ a + ⃑ b = ⃑ c . Show work. (10 points) Ax + bx = cx  -10.0 + 5.0 = -5.0 Ay +By = Cy  30.0 + -10.0 = 20.0 5. Two vectors are being added, one at an angle of 20.0 ° , and the other at 80.0 ° . The only thing you know about the magnitudes is they are both positive. Will the equilibrant vector be in the (a) first quadrant, (b) second quadrant, (c) third quadrant, (d) fourth quadrant or (e) you cannot tell which quadrant from the available information? Justify your answer. (10 points) 20.0 + 80.0 = 100.00 Since both vectors lay within the first quadrant range (as seen in the diagram), this indicates the resultant is in the first quadrant as well. As a result, the equilibrant is in the third quadrant since it is the opposite of the resultant. 2