Chapter 15 49) A piece of lead has the shape of a hockey puck, with a diameter o
ID: 2155823 • Letter: C
Question
Chapter 1549) A piece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm. If the puck is placed in a mercury bath, it floats. How deep below the surface of the mercury is the bottom of the lead puck?
Explanation / Answer
.A piece of lead (p = 11300 kg/m3) has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm. If the puck is placed in a mercury (p = 13600 kg/m3) bath it floats. How deep below the surface of the mercury is the bottom of the lead puck? ___ cm I know an easy way to determine the fraction that is under water! The Density ratio equals the fraction of volume of the object that is under the surface of the liquid. Density ratio = Density of object / Density of liquid Density ratio = 11300 / 13600 The fraction that is under the surface of the liquid = 113/136 This is the fraction of volume of the hockey puck that is under mercury. Since the puck is 2.5 cm high, the fraction of the height that is under mercury = 113/136 So, the height of the puck that is under mercury = 113/136 * 2.5 This is also how deep below the surface of the mercury the bottom of the lead puck is! How deep below the surface of the mercury is the bottom of the lead puck? 113/136 * 2.5 cm Net force up = Buoyant force – Weight The net force is the force that is pushing a floating object up. If the Buoyant force > Weight, the object will float. As the buoyant force increases, more of the object is above the surface. Volume of lead = p * radius^2 * height Mass of lead = Volume * Density Radius = ½ * diameter = ½ * 7.5 cm = 3.75 cm = 0.0375 m Height = 2.5 cm = 0.025 m Volume = p * 0.0375^2 * 0.025 Mass = (p * 0.0375^2 * 0.025) * 11300 Weight of lead = (p * 0.0375^2 * 0.025) * 11300 * 9.8 Buoyant force = volume of puck under surface * Density of Hg * 9.8 Buoyant force = volume of puck under surface * 13,600 * 9.8 As the puck sinks into the mercury, the entire area of the bottom is under and part of the height is under. Volume under = p * 0.0375^2 * h Buoyant force = p * 0.0375^2 * h * 13,600 * 9.8 Buoyant force = weight p * 0.0375^2 * h * 13600 * 9.8 = (p * 0.0375^2 * 0.025) * 11300 * 9.8 divide both sides by (p * 0.0375^2 * 9.8) h * 13600 = 0.025 * 11300 h = 0.025 * 11300 ÷ 13600 h = 0.025 * 113 ÷ 136 same answer as before now you know 2 methods
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.