Torque

The above shows a 3 3 m rod fixed by the rotation axis at the point where the internal division ratio is 1 : 2. 1:2. If three forces indicated by the three red arrows-- 20 20 N, 40 40 N, F--are acting and the rod does not rotate, what is the magnitude of F F ?

10 2 10\sqrt{2} N 15 2 15\sqrt{2} N 30 30 N 15 15 N

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2 solutions

Provided the rod does not rotate implies there is a momentum equilibrium among all the forces involved. Therefore, the equilibrium at the axis is the result of:

20N x sin(45) x its distance to axis + F x its distance to the axis - 40N x sin (45) x its distance to the axis.

20N x 2 \sqrt{2} / 2 x 1 + F x 2 = 40N x 2 \sqrt{2} / 2 x 2

10N x 2 \sqrt{2} + 2F = 40N x 2 \sqrt{2}

2F = 30N x 2 \sqrt{2}

F = 15N x 2 \sqrt{2} .

Aavruti Porlikar
Apr 16, 2014

The free body diagram represents the following equality of torques: (1)20 sin45+(2)F=(2) 40sin45. which yields F=15 2 \sqrt{2}

I can't understand

Satyam Thakur - 1 year, 7 months ago

why don't we consider its weight, mg?

Murphy Sun - 4 months, 3 weeks ago

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