A. Two kids are playing by a fresh-water reservior that was created by placing a

Question

A. Two kids are playing by a fresh-water reservior that was created by placing a dam across a gorge. They both climb into a cylindrically-shaped barrel (1 m diameter, 1 m height) and jump into the water. They notice that they are just barely floating, with the water level just at the top of the barrel. What is the combined mass of the two kids?

B. TO avoid sinking, one of the kids climbs out of the barrel. He notices that there is a leak in the dam coming through a hole that is 2.00 m delow the surface of the water. If he exerts a force of 13 N with his hand to successfully plug the leak, what was the diameter of the hole?

Explanation / Answer

A.diameter of cylindrically-shaped barrel is d = 1 m

radius is r = (d/2) = (1/2) = 0.5 m

height is h = 1 m

volume of the barrel is

V = pi * r^2 * h

let p be the density of barrel

we know that

p = (m/V)

where m is combined mass of the two kids

or m = p * V

B.height of the hole below the surface of water is h = 2.00 m

force exerted by the kid is F = 13 N

pressure of water is

P = pgh

where p is density of water(1000 kg/m^3) and g = 9.8 m/s^2

we know that

P = (F/A)

where F is force exerted by the kid and A is area of the hole

or A = (F/P)

or pi * (d^2/4) = (F/P)

or d^2 = (4F/pi * P)

or d = (4F/pi * P)^1/2

where d is diameter of the hole

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