Question

2. The rotation of the earth might have an effect on g measured on the Earth. Let's imagine standing on a scale at a latitude on the Earth. Taking the rotation of the Earth into account, we want to evaluate the value of "g" that a scale would read that would be measured as the normal force from the scale (the apparent weight), to be m'g'. a. For a person standing at the north pole: i. Draw your free body diagram. It should include 1. Gravitational Force. 2. Acceleration, as worded, is only to keep in circular motion. 3. Normal force. Direction is inferred from the gravitational force and acceleration and may not be known exactly. i. For a person with a mass of 100 kg, calculate the magnitude of the normal force and then "g' to at least 5 digits. b. Repeat for someone at the equator. C. Repeat for someone at Chemeketa Salem Campus latitude --45° N) d. Assuming all three peoples had the same mass, who would feel the heaviest?

Answer 1

At first I have given the natural case so that u will understand the theory first !!.. then I have focused on special cases:-

sw mw²rcoso +N) 1o mwep

(mw²rcoso +N) mw Let earth is revolving arover es revolving around with an angular speed We have to find acceleration due to gravity at & fpoint. 2 where radius & no = coso ur-Roso. is shown in (2) Forces acting on mass mo at mwro Coso + N = geranitational force Cos? Component of centrifugas force morgo Normal force. N = mg - mazy loso Nang - mwek Caro tet, Appearent acceleration of misgo mg & mg am wre Costo Now - w - - = 7.27x16 gadis R = (6.37x106) m. w2R = 0.0386/gr

(N+mworroso (a) For a person in north pole. - ► mwy here o=90 mg Namg = 100 x 4.807 - 980.70 N g'=g? (N = mg some one in For equatos . here oog i N= mga mw² Roro. mwiscoso +N = n 9 - ท 4.3" R - mg - m (0.0396) 725 W²R = 24x3600 • 100 (9-010336) - 977.33N X(6.37x10) = 0.0336 m/ morcos 454) mw²so © Namg-mweR(Coz. 450)? cm (g- 0:03 36 x - 2) = 100(9-80.7 -0.0168) Y-R Cos 979.02 N for a g -9.8070 m/s © -- g' = 9.7753 m/s2 ☺ - g' - 9.7902 m/s2 (1) so, at north pole person will feel heaviest.