Answer:
a) i) x = 0.25 m, ii) x = 0.10 m, iii) x = 0.050 m
b) i) x = 0.40 m
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
