The 78 kg student in the figure (Figure 1) balances a 1200 kg elephant on a hydr

Question

The 78 kg student in the figure (Figure 1) balances a 1200 kg elephant on a hydraulic lift. What is the diameter of the piston the student is standing on? Express your answer to two significant figures and include the appropriate units. Enter your answer using dimensions of distance. When a second student joins the first, the height difference between the liquid levels in the right and left pistons is 40 cm. What is the second student's mass? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

here,

mass of student, ms = 78 kg

mass of elephant, me = 1200 kg

Radius of elephant side, re = 2/2 = 1 m

Part a:
the elephant and the student are on the same level, so we can assume:

pressure on student side = Pressure on elephant side

F1/A1 = F2/A2

ms*g/(pi*r1^2) = me*g/(pi*r2^2)

78*g/(pi*r1^2) = 1200*g/(pi*(1)^2)

radius on student side, r1 = 0.255 m

diameter on student , d1 = 0.51 m

part B :
if the student fall 0.4 m then the elephant will rise 0.4 m

Then
net difference, h = (0.255/2)^2 + 0.4
net difference, h = 0.416 m

so,

Gravity force duw to student/area = rho * g * h

mass of second student, m = rho * h * pi * (d^2/4)

mass of second student, m = 900 * 0.416 * pi * (0.51^2/4)

mass of second student, m = 76.483 kg

This ans soley depend upon density of OIL

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