The weight of a metal bracelet is measured to be 0.13000 N in air and 0.09500 N when immersed in water. Find its density. kg/m3

To find the density of the metal bracelet, we need to use the principle of buoyancy, which states that the buoyant force (the force that a fluid exerts on an object submerged in it) is equal to the weight of the fluid displaced by the object.

Here are the steps to find the density:

1. First, we need to find the volume of the bracelet. We can do this by using the formula for buoyant force, which is the weight of the bracelet in air minus its weight in water. This gives us the weight of the water displaced by the bracelet, which is equal to the volume of the bracelet (since the density of water is 1 g/cm^3 or 1000 kg/m^3).

   So, the volume V of the bracelet is (0.13000 N - 0.09500 N) / (9.8 m/s^2) = 0.00357 m^3.

2. Next, we find the mass of the bracelet. The weight of the bracelet in air is the force of gravity acting on it, so its mass m is its weight divided by the acceleration due to gravity (9.8 m/s^2).

   So, the mass m of the bracelet is 0.13000 N / 9.8 m/s^2 = 0.01327 kg.

3. Finally, we find the density of the bracelet by dividing its mass by its volume.

   So, the density ρ of the bracelet is 0.01327 kg / 0.00357 m^3 = 3720 kg/m^3.

Therefore, the density of the metal bracelet is approximately 3720 kg/m^3.