Defining a Fluid A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid. Both liquids and gases are considered fluids because they can flow and change shape. Liquids have a definite volume; gases do not.

Density and Buoyant Force The buoyant force is the upward force exerted by a liquid on an object immersed in or floating on the liquid. Buoyant forces can keep objects afloat.

A rock weighs 2. 25 newtons when suspended in air A rock weighs 2.25 newtons when suspended in air. In water, it appears to weigh only 1.8 newtons. What is the buoyant force exerted on the rock?

2.25 N – 1.8 N = 0.45 N

You suspend a brass ring from a spring scale. Its weight is 0 You suspend a brass ring from a spring scale. Its weight is 0.83 N while it is suspended in air. Next, you immerse the ring in a container of light corn syrup. The ring appears to weigh 0.71 N. What is the buoyant force acting on the ring in the light corn syrup?

Buoyant Force

Density and Buoyant Force Archimedes’ principle describes the magnitude of a buoyant force. Archimedes’ principle: Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object. FB = Fg (displaced fluid) = mfg magnitude of buoyant force = weight of fluid displaced

Displaced Volume of a Fluid

A beach ball has a volume of 14,130 cm3 A beach ball has a volume of 14,130 cm3. This means that if you push the ball underwater, it displaces 14,130 cm3 of water. Archimedes principle tells us that the buoyant force on the ball is equal to the weight of that water. Because the weight of 14,130 cm3 of water is 138 newtons, the buoyant force acting on the beach ball is 138 newtons. In air, a beach ball weighs 1.5 newtons. However, if you measure the weight of a floating beach ball in water, a spring scale reads 0.0 newtons. The apparent weight of the ball is 0.0 newtons. The buoyant force acting on the floating beach ball is equal to: (The gravitational force acting on the ball) - (Apparent weight of ball in water) The buoyant force acting on the floating beach ball is equal to the gravitational force pulling the ball downward. The floating ball displaces only 153 cm3 of water. 153 cm3 of water weighs1.5 newtons. The ball displaces an amount of water equal to its own weight.

Density and Buoyant Force For a floating object, the buoyant force equals the object’s weight. The apparent weight of a submerged object depends on the density of the object. For an object with density rO submerged in a fluid of density rf, the buoyant force FB obeys the following ratio:

Sample Problem Buoyant Force A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown made of pure gold? Explain.

Classwork Answers Sink Float 0.12 N 0.10 N The light corn syrup has greater buoyant force than the vegetable oil. 0.13 N The buoyant force would be smaller if the gold cube were suspended in water. Water is less dense than the molasses.