A rock sample hangs from a spring balance. The balance registers 37 N in air, 15 N when the rock sample is completely immersed in water.  What is the density, in kg/m3, of the rock sample?

Sure, here are the steps to solve this problem:

1. First, we need to find the volume of the rock. We can do this by using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. In this case, the buoyant force is the difference between the weight of the rock in air and the weight in water, which is 37 N - 15 N = 22 N.

2. Since the weight of the water displaced is equal to the buoyant force, we can find the volume of the rock by dividing the buoyant force by the density of water. The density of water is 1000 kg/m^3, so the volume of the rock is 22 N / (1000 kg/m^3 * 9.8 m/s^2) = 0.00224 m^3.

3. Now that we have the volume of the rock, we can find its density by dividing its weight in air by its volume. The weight of the rock in air is 37 N, so its mass is 37 N / 9.8 m/s^2 = 3.78 kg. Therefore, the density of the rock is 3.78 kg / 0.00224 m^3 = 1687.5 kg/m^3.

So, the density of the rock sample is approximately 1687.5 kg/m^3.