Some topics of discussion on this problem:
- Step No. 1: FBD. Here you need to draw an FBD of the gondola. Note that we are allowed to ignore the mass of arm AB. With this, the force of arm AB (F_AB) on the gondola acts along line AB (AB is two force member). Also, it is suggested that you use a cylindrical coordinate system (unit vectors e_R, e_phi and k as shown above). Note that e_R points out along a perpendicular line from the axis of rotation from O to B. R is the radial distance from O to B.
- Step No. 2: Newton's 2nd law. Here sum forces in the e_R and k directions. This gives two scalar equations.
- Step No. 3: Kinematics. Note here that R is a constant for all time. Therefore, R_dot and R_dot_dot are zero. In addition, since B remains at a constant height, then z_dot_dot is also zero. The rotation rate N is phi_dot.
- Step No. 4: Solve. The two equations from Step No. 2 are in terms of two unknowns: F_AB and N. Solve.
2 comments:
In my FBD I Have the force due to the arm and gravity.
Are there other forces?
That's it: force due to arm has both e_R and k components whereas weight is only in the -k direction.
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