If I travel to Mexico and buy a 55g gold braclet for 20 dollars and take the braclet and submerge it in water starting out with 50cc and after it is submerged in the water it is 52.8cc. What is the buoyant force on the braclet? I also need to know if the braclet is real gold. The density of gold is 19.3g/cc. Please help me with a step by step formula for these questions with the answers.

Archimedes's principle states that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid the body displaces.

In this case. 2.8 cc of water is displaced and its weight 2.8 g. Hence the net buoyant force = 2.8 gf
Now the density of the piece = 55/2.8 ~=19.64 g/cc which greater than the given density of gold. Hence we conclude that the piece is not genuine. May contain traces of iridium which is heavier than gold and costs about 15 to 20% less than gold.

To calculate the buoyant force on the bracelet and determine if it is real gold, you can follow these steps:

1. Calculate the volume of the bracelet:
The volume can be calculated using the initial and final volume of water displaced when the bracelet is submerged. Subtract the initial volume from the final volume to get the volume of the bracelet.
Volume of bracelet = Final volume - Initial volume = 52.8 cc - 50 cc = 2.8 cc.

2. Calculate the mass of the bracelet:
Mass = Density × Volume. Since the density of gold is given as 19.3 g/cc, multiply it by the volume calculated in the previous step.
Mass = 19.3 g/cc × 2.8 cc = 54.04 g.

3. Calculate the weight of the bracelet:
Weight is the force acting on the bracelet due to gravity. Use the formula Weight = Mass × Acceleration due to Gravity.
Acceleration due to Gravity is approximately 9.8 m/s^2.
Weight = 54.04 g × (1 kg/1000 g) × 9.8 m/s^2 = 0.530 kg × 9.8 m/s^2 = 5.19 N.

4. Calculate the buoyant force:
The buoyant force is equal to the weight of the fluid displaced by the submerged object. In this case, the fluid is water.
Buoyant Force = Weight of fluid displaced = Weight of water displaced.
The weight of water displaced is equal to the weight of bracelet when it is fully submerged (assuming no air bubbles are trapped).
Buoyant Force = Weight of the bracelet = 5.19 N.

To determine if the bracelet is real gold:
A 55 g gold bracelet bought for $20 seems unusual as gold is generally quite expensive. Therefore, it is likely that the bracelet is not real gold. However, this conclusion is based on the price and not on the buoyant force calculation. The buoyant force calculation does not provide information about the authenticity of the bracelet.