Question

You hold still a uniform, 28 g pen horizontal with your thumb pushing down on one end and your index finger pushing upward 3.5 cm from your thumb. The pen is 14 cm long. Find the magnitude of the two forces?

Answer 1

Given

   mass of pen m = 28g = 0.028 kg
   length of the pen l = 14 cm = 0.14 m

the centre of mass of pen is at its centre = 0.07 m

thumb pushing down on one end and finger pushing upward at 0.035 m from one end

the force applied by finger is (torque about centre)

       0.028*9.8*0.07/0.035 = 0.5488 N

the force of thumb is 0.5488 N - 0.028*9.8 N = 0.2744 N

magnitude of the forces is finger = 0.5488 N, thumb = 0.2744 N