Question

1. In the space below,

a. state Archimedes’ Principle

b. define density

c. Mathematically, derive an equation based on this laboratory that uses Archimedes principle to measure the density of an object in terms of measurable quantities. Make sure the density of the object is NOT in terms of the unknown volume of the object in question. You can assume you know the density of water.

d. Be sure to draw a free-body diagram of the mass attached to the string

** Note the tension of the string while one object is submerged measures what we call the buoyant mass, mb, times gravity, T = mbg. Not submerged, T = mog, where mo is the mass of the object.

2. Derive an equation for determining the density of a floating/wooden object using Archimedes’ Principal. No free-body diagram is needed.

3. Finally, derive an equation using Archimedes’ Principal showing how the density of a liquid can be measured. Your expression should be in terms of the density of water, object’s mass in water, the object’s mass in NaCl solution, and the object’s mass in air (i.e. in terms of the quantities in Table 1). No free-body diagram is needed.

Answer 1

a

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.

b

Density is defined as the ratio between mass and volume or mass per unit volume. It is a measure of how much stuff an object has in a unit volume (cubic meter or cubic centimeter).

c