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Solved: A certain hydraulic system is designed to exert a
Chapter 11, Problem 27(choose chapter or problem)
Problem 27PE
A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the slave cylinder to the area of the master cylinder? (b) What must be the ratio of their diameters? (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.
Questions & Answers
QUESTION:
Problem 27PE
A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the slave cylinder to the area of the master cylinder? (b) What must be the ratio of their diameters? (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.
ANSWER:
Solution 27PE:
Step 1 of 3:-
The pressure can be written mathematically as,
-------------------(1)
Where, is the applied force and
is the area of contact.
Let’s call the pressure by the master cylinder, and the pressure by the slave cylinder as
.
The forces let’s say and
and the areas are
and
.
So, according to equation (1),
------------------(2)
a)