A uniform meter ruler is balanced at its midpoint

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

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

graph question answered .. you think better when you are relaxed and happy