Question

In Figure below, a ball of mass m is connected by means of two massless strings to a rotating rod. The top string is length L. The strings are tied to the rod with separation d=L/2, and are taut. Rotating rod A) Draw and label all the forces on mass m. (6 pts.) B) Determine the angle between the upper and lower string at the ball. (3 pts.) C) What is the model for the radius of the circular path, the only variable should be L? (3 pts.) D) Write a model for the speed of the mass in terms of the following quantities: gm, L, and tension in the lower string(12 pts.) E) At what speed will the two tensions be equal? Write the model. (5 pts.) F) Model the minimum speed, such that the tension in the lower string goes to zero (5 pts.) G) If L-1 m,m 1 kg, and the ball completes 45 revolutions in one minute, what is the speed of the ball in m/s? (4 pts.) H) At the speed in G, what are the numerical values of the two tensions? (5 pts.) 1) Using numbers in G for mass and length, what is the number of revolutions per minute that would correspond to the minimum speed in part F. (2 pts.)

Answer 1

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a) FBD of 'm' FBD YA sino = d = t = 1 (@=30) And c) Radins of circular path ,R=LCBO = L Cop 35 = 33 d) Ti + Taso= mv 0 along vertical, Tz Siho= mg Iz = mg - 20 Tot in the 290 = mas Titang sino .Xogo = Tit mg x cat 30 = mv² LG630 V = LX53 (T1+1.732 mg). g = 10.866L (Tit 1-732mg) Twe m e) TI = T2 = mg - zing DV from 2kg + 249 925 - Ylv? V = $31,6742 And 9 31.674 L Lozo