Answer:
58.32 N
Explanation:
Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
where r is the radius of the circle.
The cylinder has a radius of 0.02 m, its area is;
[tex]A_{1}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.02)^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x 0.0004
= 1.2571 x [tex]10^{-3}[/tex]
Area of the cylinder is 0.0013 [tex]m^{2}[/tex].
The safety valve has a radius of 0.0075 m, its area is;
[tex]A_{2}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.0075)^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x 5.625 x [tex]10^{-5}[/tex]
= 1.7679 x [tex]10^{-4}[/tex]
Area of the valve is 0.00018 [tex]m^{2}[/tex].
From Hooke's law, the force on the safety valve can be determined by;
F = ke
[tex]F_{2}[/tex] = 950 x 0.0085
= 8.075 N
Minimum force, [tex]F_{1}[/tex], required can be determined by;
[tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]
[tex]\frac{F_{1} }{0.0013}[/tex] = [tex]\frac{8.075}{0.00018}[/tex]
[tex]F_{1}[/tex] = [tex]\frac{0.0013 *8.075}{0.00018}[/tex]
= 58.32
The minimum force that must be exerted on the piston is 58.32 N.
