Question

A 12-inch ruler rests on your right index finger at the 6-inch mark. (a) What forces are present? (b) Write the first and second equations of equilibrium fully and show that both conditions are satisfied. (c) If a 1 lb. object is put on at the three-inch mark from the left edge of ruler, at what distance would a 2 lb. object need to be placed at to balance it (measured from the center pivot point)?

Answer 1

(a)

There is weight of ruler acting vertically downwards just at the middle of ruler and there is normal force from the finger acting vertically upwards

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(b)

first condition of equilibrium

net torque = 0

as there is no force to rotate the ruler about its axis, net torque = 0

second condition of equilibirum

net force = 0

all the vertical forces are balanced

______________________

(c)

take torque about the pivot point ( where index finger is)

1 * 3 = 2 * x

x = 3 / 2

x = 1.5

so,

2 lb must be placed at 7.5 inch mark