A cylinder of radius 35 cm is filled with an ideal fluid and is connected by a h

Question

A cylinder of radius 35 cm is filled with an ideal fluid and is connected by a hose to a second cylinder of radius 50 cm. A mass of 40 kg is placed on the top of the smaller cylinder.

a) If the height of the two cylinders is exactly the same, what mass should be placed on the second cylinder to balance the system?

b) Unfortunately, you discover that the only extra mass you have is another 40 kg block! If you place the extra 40 kg block on the second cylinder, what is the height of the top of the second cylinder compared to the height of the first if the fluid is known to have a density of 550 kg/m3?

Explanation / Answer

a) Oil fills the left side of the cylinder to a depth of 29.0 cm

Volume of oil added on left = (pi ((35^2)) x 29 = 111548.5cc.
Mass of oil = (111548.5 x 0.550) = 61351.675.

If the column height is TO BE exactly the same, a mass of ((1 - 0.550) x 61351.675)g = 27608.25 g bor 27.608 kg, would need to be placed on the left side

b) Rise height of water on right = 61351.675/ ((50^2) x pi) =7.79 cm.

height of the top of the second cylinder compared to the height of the first =29-7.79=21.21 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.