Amodel hydroelectric power station produces just enough electric power to light a 6.0 w lamp. the model is found to be 80% efficient at converting the potential energy store of the water into electrical work. what is the input power of the water running through the pipes?

You said that the useful output power from the model is 6 watts.  You also said that the model is 80% efficient.  We have no reason to doubt your word, so we know that

(useful output) / (input power) = 80% or 0.8

(6 watts) / (input power) = 0.8

Multiply each side by (input power): 6 watts = (0.8) (input power)

Divide each side by 0.8 :  Input power = (6 watts/ 0.8)

Input power =  7.5 watts

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