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Cable supporting a boom & a sphere rolling down an incline

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26) A 1200 N uniform boom is supported by a cable; one end of the cable being attached to a wall and the other end to top of the boom. The cable is perpendicular to the boom. One end of the boom is attached to a hing on the ground and is leaning away from the wall at an angle of 65 degrees to the ground. A 2000 N weight hangs from its top. Find the tension in the supporting cable and the components of the reaction force exerted on the boom by the hinge.

44) A 240 N sphere, 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 37 degrees with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest?

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The problems have been solved in a step by step fashion bring out the fundamental physics principles involved.

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The arrangement as described in the problem is shown in the fig.. The weight of the boom (1200 N) acts at the centre of gravity (mid point of the boom). The forces acting on the boom are : Weight of the boom, 2000 N weight suspended from top of the boom, Rx and Ry horizontal and vertical components of the reaction of the hinge on the boom.

For equilibrium, moment of the forces about the hinge = 2000 x L cos 65O + 1200 x L/2 cos 65O - T x L = 0 where L = length of the boom ............(1)

[As the forces Rx and Ry pass through the hinge, their moments about the hinge are zero]

Solving (1) we get : T = 2000 x cos 65O + 1200/2 cos 65O = 1099 N

To determine Rx and Ry we equate net force on the boom in the horizontal direction and net force on the boom in the vertical direction equal to zero (for equilibrium).

For vertical direction : Ry - 1200 - ...

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