Answer : The correct answer for force = 11.745 N .
Hydraulic system is a system which is operated by moving liquid in a definite area which is under pressure . It uses the force which is produced due to difference in pressure at two ends of a system .
It basically uses oil or water ( incompressible liquids ) , which can relocate the force from one area to other in the fluid .
The force around different areas can be calculated using Pascal's Principle.
Pascal's Principle : It states that if there in increase in pressure in any area in fluid , there will be equal to increase in pressure at other area . It can be expressed as :
[tex] P1 = P2 [/tex] ---------Equation (1)
, where P1 = pressure in one area P2 = pressure in other area .
Pressure is defined as force acting per unit area . Hence , Pressure and force can be related as :
[tex] Pressure(P) = \frac{Force }{area } [/tex]
Where unit of pressure= pascals(p) Force= newton(N)
Area = meter square (m²)
On plugging value of pressure in equation (1) :
[tex] \frac{F1}{A1} = \frac{F2}{A2} [/tex] ------ Equation (2)
Where , F1 = force at one area A1 = area of one area
F2 = force at other area A2 = area of other area
Given : F 1 = 81 N A1 = 5 cm² or 0.0005 m² ( 1 m²= 10000 cm²)
F2 = ? A2 = 725 cm² or 0.0725 m²
Plugging these value in equation (2) :
[tex] \frac{81 N}{0.0005 m^2} = \frac{F2}{0.0725 m^2} [/tex]
Multiplying both side by 0.0725 m²
[tex] \frac{81 N}{0.0005 m^2} * 0.0725 m^2 = \frac{F2 }{0.0725 m^2} * 0.0725 m^2 [/tex]
F2 = 11,745 N
Given:
Surface area at the narrow end, A1 = 5.00 cm2
Force applied at the narrow end, F1 = 81.0 N
Surface area at the wide end, A2 = 725 cm2
To determine:
Force F2 applied at the wide end
Explanation:
Use the relation
F1/A1 = F2/A2
F2 = F1*A2/A1 = 81.0 N * 725 cm2/5.00 cm2 = 11,745 N
Ans: (b)
The force applied at the wide end = 11,745 N
