Problem 3/107 Page 166, Engineering Mechanics - Dynamics, Meriam and Kraige, 4th Edition

Given: Collar of mass m sliding on a circular frictionless track of radius R and acted on be a constant force F.  The collar is at rest at the top of the track.

Find: The speed of the collar when it reaches its rightmost position.

Parameter Values:
m = 0.5 kg
F = 5 N ( cos 30 i + sin 30 j ) = 5 3^1/2 /2 N i + 2.5 N j
R = 0.2 m

1. Mechanical System: Collar at it travels from top to rightmost position.

2. Free Body Diagram: Not included.  Would show weight acting vertically downward, the constant applied force F, and a normal force from the track.

3. Equations:
Work = -m g Dh (gravity) + F . Dr (constant force) + 0 (force normal to motion)
          = -m g (-R) + Fx R - Fy R
          = ( 0.5 9.81 0.2 + 2.5 3^1/2 0.2 - 2.5 0.2 ) N m = 1.347 N m

D Kinetic Energy = 1/2 m ( vB² - 0 ) = 0.25 kg vB²

4. Solve:

1.347 N m = 0.25 kg vB²

vB = (1.347/0.25)^1/2 m/s = 2.32 m/s