Cylinder says "Don't roll. Just hang on."
Two uniform solid cylinders A and B each of mass are connected by a light spring of force constant at their axles and are placed on a fixed wedge as shown in the figure. The coefficient of friction between the wedge and the cylinders is .
If is the elongation in the spring at equilibrium then find .
Take .
The answer is 8.487.
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1 solution
In equilibrium, there will be no torque about the center of mass, and so the frictional forces must be zero.
Say the spring makes an angle θ with the horizontal. Then considering the net force along the slope for mass A gives:
sin ( π / 3 ) m g = k x cos ( π / 3 − θ )
and considering the net force along the slope for mass B gives:
sin ( π / 6 ) m g = k x sin ( π / 3 − θ )
Square each side of the equations, add the left sides and right sides, then take the square root, and you will see m g = k x so that 1 0 0 x = 1 0 0 k m g = 4 . 9 3