Respuesta :
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
The area of the input piston will be 0.00167 square meters, the work done in lifting the car will be 4193.78 J, the height moved by car in each stroke will be 0.6035 cm, the number of strokes required to lift the car by 45 cm will be 74.57, and the energy conservation is justified.
Given information:
Mass of the car is [tex]m=950[/tex] kg
The lift of the car is [tex]h=45[/tex] cm.
The diameter of the output piston D is 23 cm.
The input force f is 375 N.
Let the output force be F and the input piston diameter be d.
Hydraulic lift follows Pascal's principle.
(a)
So, the area of the input piston will be calculated as,
[tex]\dfrac{F}{\frac{\pi}{4}D^2}=\dfrac{f}{\frac{\pi}{4}d^2}\\\dfrac{\pi}{4}d^2=\dfrac{f\frac{\pi}{4}D^2}{mg}\\\dfrac{\pi}{4}d^2=A=0.00167\rm\;m^2[/tex]
(b)
The work done in lifting the car will be,
[tex]W=mgh\\W=950\times 9.81\times0.45\\W=4193.78\rm\;J[/tex]
(c)
The input piston moves 15 cm in each stroke.
The height h' moved by car in each stroke will be calculated as,
[tex]mgh'=f\times 0.15\\h'=0.006035\rm\;m=0.6035\rm\;cm[/tex]
(d)
The number of strokes required to lift the car by 45 cm will be,
[tex]n=\dfrac{h}{h'}\\n=\dfrac{45}{0.6035}\\n=74.57[/tex]
(e)
The energy is conserved when output work is equal to input work.
So, the energy conservation can be verified as,
[tex]W_i=W_o\\f\times0.15\times n=mgh\\375\times 0.15\times74.57=950\times 9.81\times0.45\\4194.28\approx4194.1[/tex]
The input and output works are approximately equal. The value isn't exactly equal because of the rounding-off.
So, energy conservation is justified.
Therefore, the area of the input piston will be 0.00167 square meters, the work done in lifting the car will be 4193.78 J, the height moved by car in each stroke will be 0.6035 cm, the number of strokes required to lift the car by 45 cm will be 74.57, and the energy conservation is justified.
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https://brainly.com/question/2590504
