Answer:
A) 100
B) 10
C) 0.01
Step-by-step explanation:
Let
Fs = force on slave cylinder
Fm = force on master cylinder
Given that the designed to exert a force 100 times as large as the one put into it. That is
Fs = 100 Fm
Using Pascal's law
Fs/As = Fm/Am
100Fm/As = Fm/Am
100/As = 1/Am
Cross multiply
As= 100Am
As/Am = 100
b) What must be the ratio of their diameters
Using their areas ratio, area of a cylinder is πr^2
A = πr^2 = π(D/2)^2
π(Ds/2)^2 ÷ π(Dm/2)^2 = 100
(Ds/2)^2 ÷ (Dm/2)^2 = 100
(Ds/Dm)^2 = 100
Ds/Dm = 10
(c) By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? Assume no losses to friction
Let us consider the workdone at the input and at the output.
Work done = force × distance
Fs × Hs = Fm × Hm
100Fm × Hs = Fm × Hm
100Hs = Hm
100Hs/Hm = 1
Hs/Hm = 1/100
Hs/Hm = 0.01