Previous exam question. Please break it down. Don\'t even know where to start. A

Question

Previous exam question. Please break it down. Don't even know where to start.

A water system is closed by two cylindrical pistons (see the drawing below). The first (small) piston has a radius of 35cm, while the second (large) piston has a radius of 2m. On the large piston a car of mass M=1.65tons is positioned. (In the following, ignore the weight of the pistons and assume water to be an incompressible fluid; 1ton=1000kg).

(a) What force needs to be applied to the small piston to balance the weight of the car? (b) How much work is required to lift the car by 10cm, and by what displacement has the small piston to be pushed down?

Ans: 8.) (a) 495N (b) 1617J, 3.27m

Explanation / Answer

a) Pressure on the large piston = Force/ large area = 1.65*1000*9.8/(pi*2*2) =1286.77 Pa

Force needed to applied = pressure* small area because pressure is same in incompressible liquid

= 1286.77 * (pi*0.35*0.35) = 495 N

b) Work done = mgh

= 1650*9.8*0.10 = 1617 J

distance moved by small piston = Work done / Force on small piston

= 1617/495

= 3.27 m

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