Physics help?

Question

Consider the 100% efficient hydraulic system below used to lift a boat: (no pic)


If the boat weighs 1600 N and must be lifted 0.8 meter (dout), how far down (din) must the input piston be pushed using a force of 500 N ?

Answer 1

I already answered this exact question, but I'll do so again.

The work done on one piston equals the work done by the second piston on the boat.

W = F*x
where W = work, F = force, x = distance

So, the work done on the boat by the second piston is
W = (1600 N) * (0.8 m)
W = 1280 Nm

You must do the same amount of work on the input piston, so we know that:
W = 1280 Nm = (500 N) * (x)
x = 2.56 m

Answer 2

If the system is 100% efficient, then the work you put in (W_in) is equal to the work you get out (W_out).

Work is equal to force x distance.

You can calculate the W_out because they give you the distance (dout) and the force_out (the weight).

They also give you the force_in (500N).

So, set W_in equal to W_out, and just solve for d_in.