4.6 Suppose frame B = (O', b1, b2, b3) is travelign in the e1 direction at a constant speed of v0 with repect to stationary frame I = (O, e1, e2, e3) as shown in Figrue 4.19. Mass mp is connected to point O' by a spring with spring constant k and rest length r0. The spring can freely pivot about O'. Assume that the positions of O and O' are the same at time t = 0.

Please solve all part (a-e) clearly and completely.

Transcribed Image Text:

Suppose frame B= (0', b₁,b2, b3) is traveling in the e, direction at a constant speed of à respect to stationary frame I = (0, e₁, 2, 3), as shown in Vo with Figure 4.19. Mass m p is connected to point O' by a spring with spring constant k and rest length ro. The spring can freely pivot about O'. Assume that the w positions of O and O' are the same at time t = 0. 4.6 4.7 0 B 4 k www Vo Figure 4.20 shows ni Pt Figure 4.19 Problem 4.6. mp P a. Using the coordinates of your choice, find the position rp/o and velocity Tvp/o of the mass with respect to O' in I. [HINT: Introduce a polar frame at O'.] b. Find the position rp/o and velocity TVP/O of the mass with respect to ΡΙΟ O in I. c. Draw a free-body diagram for mass mp. (There is no gravity in this problem.) d. Find the angular momentum Thp/p of the mass with respect to O' in I. e. Show that the angular momentum of the mass with respect to O' in I is conserved, but the angular momentum with respect to O in I is not. Suppose frame B= (0', b₁,b2, b3) is traveling in the e, direction at a constant speed of à respect to stationary frame I = (0, e₁, 2, 3), as shown in Vo with Figure 4.19. Mass m p is connected to point O' by a spring with spring constant k and rest length ro. The spring can freely pivot about O'. Assume that the w positions of O and O' are the same at time t = 0. 4.6 4.7 0 B 4 k www Vo Figure 4.20 shows ni Pt Figure 4.19 Problem 4.6. mp P a. Using the coordinates of your choice, find the position rp/o and velocity Tvp/o of the mass with respect to O' in I. [HINT: Introduce a polar frame at O'.] b. Find the position rp/o and velocity TVP/O of the mass with respect to ΡΙΟ O in I. c. Draw a free-body diagram for mass mp. (There is no gravity in this problem.) d. Find the angular momentum Thp/p of the mass with respect to O' in I. e. Show that the angular momentum of the mass with respect to O' in I is conserved, but the angular momentum with respect to O in I is not.

Answer rating: 100% (QA)

Answer ngth for I frame making change of cinit vectors as ant vector are so... View the full answer