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Rod and mass system: Find velocity and tensions in the rod.

A rigid rod with negligible mass has a length L= 2.6 m. The rod can rotate freely about a fixed pivot at one end. Attached at the other end of the rod is mass M1 = 8.4 kg, and at its center is mass M2 = 3.6 kg. The system is released from vertical at rest to rotate about the pivot. SEE ATTACHMENT #1 for a diagram showing parameters.

PART a. Find the velocity V1 of the end mass, and the velocity V2 of the mass at the center as the rod passes through vertical after half a rotation.

PART b. Find the tension T1 in the rod between the masses, and also the tension T2 in the rod betwen pivot and the center mass.


Solution Preview

Step 1.
The first step of a solution is to make or refer to a careful diagram of the event.
From observation of the diagram of ATTACHMENT #1, note the following:
A. The radius of the circle described by M1 is L, and the radius of M2 is .5 L.
B. From top to bottom, the change in elevation of M1 is 2L, and that of M2 is L.
C. The tension T1, in the rod between the masses is an upward force on M1 and is also a downward force on M2.
D. The tension T2 in the rod segment between ...

Solution Summary

In a step by step solution, the problems are solved with good explanations of the workings.