Question

?homework 5 ch 5 friction SSII 2018 Problem 5.95 Constants I Periodic Table Part A While fishing. you get bored and start to swing a sinker welght fishing line The weight makes a complete circle every 0.60 s What is the angle that the fishing line makes with the vertical? [Hint As shown in the figure(Figure 1) Express your answer to two significant figures and include the appropriate units. in a circle below you on a 0.55 m piece of 18-1 Value Units n to Figure 1 of 1 O Type here Master search

Answer 1

If the angular frequency of rotation around the circle is w = 2 pi/tau, where tau = 0.6 s, then there is a centrifugal force acting on the mass m, equal to m w^2 r. If T is the tension in the cable of fishing line, then from the diagram t cos theta = m g T sin theta = m w^2 r Rightarrow tan theta = w^2 r/g Rightarrow tan theta = w^2 l sin theta/g Rightarrow cos theta = g/w^2 l Also r = l sin theta where l is the length of the fishing line Now l = 0.55 m, w = 2 pi/0.6 s = 10.47 s^- 1 Therefore cos theta = 9.8 m/s^2/(10.47 s^- 1)^2 times 0.55 m = 0.162 or, theta = cos^- 1 (0.162) = 80.65 degree