Question

Someone is using a scissors to cut a wire of circular cross section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2\alpha$. The friction coefficient between the blades and the wire, is:

• A. $\sqrt{1-\tan \alpha }$
• B. $2\cos \alpha$
• C. $\tan \alpha$
• D. $2\tan \alpha$

Answer 1

The correct option is C $\tan \alpha$

Given: someone is using a scissors to cut a wire of circular cross section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2\alpha$

To find friction coefficient between the blades and the wire,

Solution:

Torque applied to the joint of scissors is $\tau$

$Fd=\tau ⟹F=\frac{\tau }{d}$

Force that actually drives the rope forward is the sum of the two force vectors

$F_{forward}=\frac{2\tau \sin \alpha }{d}$

Sum of frictional forces on the upper anf lower part will be

$\frac{2\mu \tau \cos \alpha }{d}$

At some poitn, the forward moving force is not sufficient enough toovercome the friction

$\frac{2\mu \tau \cos \alpha }{d}=\frac{2\tau \sin \alpha }{d}⟹\mu =\tan \alpha$

is the friction coefficient between the blades and the wire