The small 3-lb block slides on a smooth horizontal surface under the action of the force in the spring and a force F . The angular momentum of the block about O varies with time as shown in the graph. When t = 6.5 sec., it is known that r = 6 in. and β = 60º. Determine F for this instant.
Text Solution
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Sol. The only moment of the forces about O is due to F since the spring force passes through O. Thus Σ M O = Fr sin β . From the graph the time rate of change of H O for t = 6.5 sec is very nearly (8 – 4) / (7 – 6) or H O = 4 ft-lb. The moment-angular momentum relation gives
[ Σ M O = H O ] F 
sin 60º = 4
F = 9.24 lb Ans.
Helpful Hint:
We do not need vector notation here since we have plane motion where since we have plane motion where the direction of the vector H O does not change.
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