In a hydraulic system, a force of 400 N is exerted on a piston with an area of 0.001 m2. The load-bearing piston in the system has an area of 0.2 m^2. Required:
a. Calculate in kPa the pressure in the hydraulic fluid induced by the applied pressure.
b. What is the magnitude of the force exerted on the load bearing piston by the hydraulic fluid?

Explanation:

Pressure on the hydraulic system is expressed as;

Pressure = Force/Area

Given

Force on the fluid = 400N

Area = 0.001m²

Pressure in the fluid = 400/0.001

Pressure in the fluid = 400,000N/m²

1N/m² = 0.001kPa

400,000N/m² = x

x = 400,000 × 0.001

x = 400kPa

Hence the pressure in kPa is 400kPa

b) Using the formula;

Pa = Pb

Fa/Aa = Fb/Ab

Pa = Fb/Ab

Fb = PaAb

Fb = 400,000(0.2)

Fb = 80,000N

Hence the magnitude of the force exerted on the load bearing piston by the hydraulic fluid is 80,000N

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a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: