V. QUESTIONS 1) In ordinary arithmetic, we can think of subtraction as \"adding

Question

V. QUESTIONS 1) In ordinary arithmetic, we can think of subtraction as "adding the negative." That is, The same is true for vector addition, A-B A -B The question is, however, what is the "negative" of a vector? We have already answered this question when we were thinking about the resultant and the equilibrant. The negative of a vector is the vector with the same magnitude but the opposite direction..."equal and opposite." Using the forces from Vector Addition 2, determine the magnitude and direction of Fi-F using both the graphical method and the components method (simply subtract the x- and y- components of F2 from those of Fi instead of adding). 2) Demonstrate graphically a case in which the difference of two vectors has greater magnitude than the sum. 3) A picture hangs on a nail as shown here. The tension, Fr, in each string is 3.5 N. That means that each string pulls on the picture with a force of 3.5 N and that each string pulls on the nail with a force of 3.5 N at the angle shown. a) What is the equilibrant or upward reaction force T. provided by the thumbtack? 3.3 5 b) What is the weight (in Newtons) of the picture? c) If the angle the strings make with the frame was decreased to 20o, the tensions in the strings would increase. Find the tension required in each string to hold up the picture. Ph ys i cs Ph un! a The nail is the equibort Upward force= Fa = TSIn 45-TSin45- Fu- 3.5sin45+ 35 sin45-4.95 N W 495 N

Explanation / Answer

Weight of the picture, W = 2T sin(45)
= 2 x 3.5 x sin(45)
= 4.95 N

c)
When the angle is reduced to 20 degrees, tension in the string has to support the same weight.
W = 2T sin(20)
T = W / (2 sin(20)
= 4.95 / [2 x sin(20)]
= 7.24 N

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