A barber’s chair with a person in it weighs 2118.0 N. The output plunger of a hydraulic system begins to lift the chair when the barber’s foot applies a force of 63.0 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

Respuesta :

Answer:5.8

Step-by-step explanation:

Given

weight of chair with person on it =2118 N

Barber applies a force of 63 N

Using pascal's law

we know pressure around both sides is equal

i.e. [tex]P_{chair}=P_{piston}[/tex]

pressure=[tex]\frac{force}{area}[/tex]

[tex]P_{chair}[/tex]=[tex]\frac{2118}{\pi \dot r_{plunger}^2}[/tex]

[tex]P_{piston}[/tex]=[tex]\frac{63}{\pi \dot r_{piston}^2}[/tex]

substituting values

[tex]\left [\frac{r_{plunger}^2}{r_{piston}^2}\right ][/tex]=[tex]\frac{2118}{63}[/tex]

[tex]\left [\frac{r_{plunger}}{r_{piston}}\right ][/tex]=[tex]\left [ \frac{2118}{63}\right ]^{0.5}[/tex]

[tex]\left [\frac{r_{plunger}}{r_{piston}}\right ][/tex]=5.798