Answer:
a. A input = 0.001669 m²
b. W= 4.193775 KJ
c. h output = 0.60357 cm
d. n = 74.55638 strokes
e. 4.1937 N = 4.1937 N
Explanation:
Hydraulic jacks lift loads using the force created by the pressure in the cylinder chamber by applying small effort. It works on Pascal's principles which explains that the pressure at a certain level and through a mass of fluid at rest is the same in all the directions.
Parameters given:
Diameter of the output piston,
d
= 0.23
m
Mass of the car, m=
950
kg
Force applied at the input piston, f
=
375
N
Height, h =
0.45
m
(a) Finding the area of the input piston:
First, we use Pascal's principle to find the area
(f ÷ A output) ÷ (f ÷ A input)
Where A= area
g = 9.81
A output = πd² ÷ 4
(f ÷ (πd² ÷ 4)) = (f ÷ A input)
[(950 x 9.81) ÷ ((3.14 x 0.23²) ÷ 4) ] = 375 ÷ A input
9319.5 ÷ 0.0415 = 375 ÷ A input
A input = 0.001669 m²
(b) Finding the work done in lifting the car 45 cm
Work done, W = force, f x distance ( which in this case is height, h)
= (950 x 9.81) x 0.45
W= 4.193775 KJ
(c) Finding how the car move up for each stroke if the input piston moves 15 cm in each stroke.
W output = W input
F x h output = F x h input
= (950 x 9.81) x h output = 375 x 0.15
h output = 0.0060357 m
h output = 0.60357 cm
(d) Finding the number of strokes that are required to jack the car up 45 cm
n = h ÷ h output
n = 45 ÷ 0.60357 cm
n = 74.55638 strokes
(e) How the energy is conserved
W output = W input
F x h output = F x h input x n
(950 x 9.81) x 0.45 = 375 x 0.15 x 74.55638
4.1937 N = 4.1937 N
