Aforce of 250n is applied to a hydraulic jack piston wth
a0.1m diameter. if the output piston, which supports the load, has a
diameter of .5m, how much weight can be lifted?

To solve this problem we will apply the Pascal principle. This law establishes that the pressure exerted on an incompressible fluid and in equilibrium within a container of non-deformable walls is transmitted with equal intensity in all directions and at all points of the fluid.

Mathematically the relationship is given as

Since it is a circular piston the area will be given as

Replacing,

Our values are given as

Replacing we have that

Therefore the wieght that can be lifted is 6250N

answer; equivalent to a one(1) horsepower motor;

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.