Question
An ore sample weighs 17.70 N in air. When the sample is suspended I by a light cord and totally immersed in water.the tension in the cord is 11.90 N. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Buoyancy.
Solution
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Julia
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Answer
Here's how to determine the total volume and density of the ore sample:**1. Calculate the Buoyant Force:**The buoyant force (Fb) is the difference between the weight of the sample in air and the tension in the cord when submerged in water.Fb = Weight in air - Tension in cordFb = 17.70 N - 11.90 NFb = 5.80 N**2. Determine the Volume of the Ore Sample:**Archimedes' principle states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object. Since the ore sample is totally immersed in water, the buoyant force is equal to the weight of the water displaced. We can use the following formula:Fb = ρwater * V * gWhere:* Fb is the buoyant force (5.80 N)* ρwater is the density of water (1000 kg/m³)* V is the volume of the ore sample (what we want to find)* g is the acceleration due to gravity (9.81 m/s²)Rearranging the formula to solve for V:V = Fb / (ρwater * g)V = 5.80 N / (1000 kg/m³ * 9.81 m/s²)V = 5.91 x 10⁻⁴ m³**3. Calculate the Mass of the Ore Sample:**We can find the mass (m) of the ore sample using its weight in air and the acceleration due to gravity:Weight = m * gm = Weight / gm = 17.70 N / 9.81 m/s²m = 1.80 kg**4. Calculate the Density of the Ore Sample:**Density (ρ) is defined as mass per unit volume:ρ = m / Vρ = 1.80 kg / 5.91 x 10⁻⁴ m³ρ = 3046 kg/m³ or approximately 3.05 x 10³ kg/m³**Therefore:*** The total volume of the ore sample is approximately **5.91 x 10⁻⁴ m³**.* The density of the ore sample is approximately **3.05 x 10³ kg/m³**.