Ahydraulic lift is used to raise an automobile of mass 1510 kg. the radius of the shaft of the lift is 8.0 cm and that of the piston is 1.0 cm. how much force must be applied to the piston to raise the automobile? \

applied force on piston is 302.308163 N

Explanation:

Given data

mass = 1510 kg

weight = 1510 × 9.81 = 14813.1 N

radius = 8 cm

piston =  1.0 cm

to find out

force

solution

we will apply here pascal principal i.e

weight of automobile / area 1  = applied force on piston / area 2

so applied force on piston = weight of automobile × area 2  / area 1

and we know that areas is proportional to square of diameter

so area 2  / area 1 = (0.01/0.08)²

so  applied force on piston = weight of automobile × (0.01/0.08)²

applied force on piston = 14813.1  × (0.01/0.07)²

applied force on piston is 302.308163 N

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.