Let\'s see how Pascal\'s law can be used to amplify a force. Suppose the hydraul
ID: 1504463 • Letter: L
Question
Let's see how Pascal's law can be used to amplify a force. Suppose the hydraulic lift shown in (Figure 1) has a small cylindrical piston with radius 5.0 cm and a larger piston with radius 20 cm. The mass of a car placed on the larger piston's platform is 1000 kg. (a) Assuming that the two pistons are at the same height, what force must be applied to the small piston to lift the car? (b) How far must the small piston move down to lift the car through a height of 0.10 m?
Engineers are designing a hydraulic lift that can be used to repair trucks with a mass of 6400 kg . What ratio of piston areas would you suggest for the design if the maximum available external force is to be 2600 N ? Express your answer to three significant figures.
Explanation / Answer
Here ,
radius , r1 = 5 cm
radius of outer , r2 = 20 cm
mass of car , M = 1000 Kg
a) let the force applied on the smaller piston is Fs
pressure at both pistons is same
M*g/(pi * r2^2) = Fs/(pi * r1^2)
1000 * 9.8/(pi * 20^2) = Fs/(pi * 5^2)
solving
Fs = 612.5 N
the force applied at the smaller piston is 612.5 N
b)
as the change in volume is same for both
pi * r1^2 * d1 = pi * r2^2 * h2
5^2 * d1 = 0.10 * 20^2
d1 = 1.6 m
the change in height of smaller piston is 1.6 m
--------------------------------------------------
let the ratio of ares A2/A1
as the pressure is same for both pistons
6400 * 9.8/A2 = 2600/A1
A1/A2 = 0.0415
the ratio of areas of pistons is .0415
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.