Question

A uniform meter ruler is balanced at its midpoint

Answer 1

a) i) x = 0.25 m, ii) x = 0.10 m, iii) x = 0.050 m

b) i) x = 0.40 m

Step-by-step explanation:

a) For this exercise we use the rotational equilibrium equation, where we assume that the anticlockwise rotations are positive.

1) L = 2W

we set our reference system in the center of the bar where the fulcrum is

∑τ = 0

W 0.50 - L x = 0

x = 0.50 W / L

we substitute the value

x = 0.50 W / 2W

x = 0.25 m

ii) L = 5W

we calculate

x = 0.50 W / 5W

x = 0.10 m

iii) L = 10 W

x = 0.50 W / 10W

x = 0.050 m

b) a new weight is placed at x₂ = 30 cm on the left side

W 0.50 + W 0.30 - L x = 0

x = (0.50 + 0.30) W / L

x = 0.80 W / L

we calculate

i) L = 2W

x = 0.80 w / 2w

x = 0.40 m