Question

Two pistons of a hydraulic ift have radi of 2.64 cm and 10.5 em. A mass of 1.85 x 10 kg is placed on the larger piston. Calculate the minimum downward force needed to be exerted on the smaller piston to hold the larger piston level with the smaller piston Number Units Hint Penalty Hint 0.0 View Hint

Answer 1

$Pressure\,\,must\,\,be\,\,to\,\,hold\,\,the\,\,larger\,\,piston\,\,level\,\,with\,\,smaller\,\,piston.\\\\ \therefore \,\,\frac{downward \,\,force\,\,on\,\,smaller\,\,piston}{crosssectional \,\,area\,\,of\,\,hydralic\,\,lift}=\frac{downward \,\,force\,\,on\,\,larger\,\,piston}{crosssectional \,\,area\,\,of\,\,hydralic\,\,lift}\\\\ \Rightarrow \,\, \frac{downward \,\,force\,\,on\,\,smaller\,\,piston}{\pi \left (\frac{2.64}{100} \right )^2\,\,m^2}=\frac{(1.85\times10^3\,\,kg)\times(9.81\,\,m/s^2)}{\pi \left (\frac{10.5}{100} \right )^2\,\,m^2}\\\\ \Rightarrow \,\,downward \,\,force\,\,on\,\,smaller\,\,piston=\frac{1.85\times10^3}{10.5^2}\times2.64^2\times9.81\,\,N$

  $\\ =116.95\times9.81\,\,N\\ \\=1147.28\,\,N$

$\therefore \,\,we\,\,need\,\,to\,\,place\,\,a\,\,116.95\,kg\,\,mass\,\,or\,\,we\,\,need\,\,to\,\,exert\,\,1147.28\,\,N\,\,force.$

$.\\\\\\\ [For\,\,any\,\,doubt\,\,please\,\,leave\,\,a\,comment]$