A tube filled with hydaulic oil has compresses air above the surface of the oil.

Question

A tube filled with hydaulic oil has compresses air above the surface of the oil. THe tube is connected to a large diameter cylinder and piston. The top of the piston is exposed to the atmosphere. There is a small-diamter pin sticking vertically upward mounted to the top of the pisto. (neglect the diameter and mass of the small pin in any calculations.) The pin is contacting a horizontal rod that is pinned at its right end. See the diagram for dimesnsions, masses and other data.

A)find the pressure acting on the bottom of the piston.

B) For the instant shown, find the vertical acceleration of the piston.

C) For the instant shown, find the angular acceleration of the rod.

Hints

-read pascals principle

-assume the piston and rod are both accelerations

-note that the mortion of the piston and the rod are related.

So i know the answers i just dont know the steps to get them so thats what i need help with;

A=333190 Pa

B=2567 m/s^2

C=1271 rad/s^2

Explanation / Answer

(A)we know P=Po +density*g*h

Po=3 atm=3*101300=303900 Pa;density=0.934*1000=934kg/m3

h=3.2m

P=303900+(934*9.8*3.2)=333190 Pa

(B) F on piston due to pressure=P*area=333190*(pie*(0.11)^2)=20516.24 N

let force due to rod be f;m is mass of rod;M is mass of piston;a is acc. of piston

ang.a be angular acc. for rod

   F-f=Ma

f*(2.69-0.62)-mg(2.69/2)=m*ang.a

also ang.a=a*(2.69-0.62)

solving above equations

a=2567 m/s^2

ang.a=1271 rad/s^2

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