If a 100 gram mass is correctly placed on the above ruler, the ruler + 100g syst

Question

If a 100 gram mass is correctly placed on the above ruler, the ruler + 100g system will remain balanced (with the 35-cm mark above the pencil and the ruler horizontal). Such a system is in equilibrium since the forces and torques are balanced and the acceleration is zero.a)Draw a diagram of the balanced system described above - showing the forces that are acting on the ruler (label your vectors). b)According to your diagram, what is the CW torque acting on the ruler? c)According to your diagram, what is the CCW torque acting on the ruler? d)Where is the 100 gram mass placed (above what ruler mark) to achieve this equilibrium?

Explanation / Answer

a)

under equilibrium condition the net toque is zero

T = r F = mg r

the CW torque acting on the ruler is

T= -m*g*r

= -0.1*9.8*(0.5 - 0.35)

= -0.147 N.m

b)

since the ruler is in equilibrium.so, net torque acting on the ruler must be equal to zero.

the CCW torque acting on the ruler is equal to negative the CW torque acting on the ruler

T = -(-0.147)

= +0.147 N.m

c)

CCW torque acting on the ruler is

T= m*g*(0.35 - x)

0.147 N m = 0.1*9.8*(0.35m - x)

0.15m = 0.35m - x

x = 0.35 - 0.15

= 0.2 m or 20 cm

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