A piece of metal with density 6.4 g/cm3 has the shape of a hockey puck, with a d

Question

A piece of metal with density 6.4 g/cm3 has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.3 cm. If the puck is placed in a bath of fluid with density 10 g/cm3, it floats.

(a) How deep below the surface of the fluid is the bottom of the metal puck?

(b) A small cube made of the same metal as the puck and with sides of length 0.95 cm is attached to the center of the puck. The puck is then inserted into the fluid, submerging the side that the cube is on. How deep below the surface of the fluid is the bottom of the metal cube?

Explanation / Answer

Here ,

density of metal , pm = 6.4 gm/cm^3

radius, r =7.5/2 = 3.75 cm

height , h = 2.3 cm

pl = 10 g/cm^3

a)

let the bottom of the metal puck is d

Using archimedes principle

pm * r^2 * h * g = pl * r^2 * d * g

6.4 * 2.3 = 10 * d

d = 1.472 cm

the surface of fluid is 1.472 cm below the metal puck

b)

Now, let the depth is d1

Using archimedes principle

pm * r^2 * h * g + pm * a^3 * g = pl * r^2 * d1 * g

6.4 * (3.75^2 * 2.3 + 0.95^3) = 10 * 3.75^2 * d1

sovling for d1

d1 = 1.511 cm

the surface of fluid is 1.511 cm below the metal puck

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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