Thread: What is the density of a rock handing from a spring scale?

A rock is hanging from a spring scale that reads 20 N. A glass of water is raised to totally submerge the rock, still suspended from the spring scale. The spring scale now reads 12.5 N. What is the density of the rock?

The spring scale's reading decreases by 7.5 N when the rock is lowered into water. That means the water pushed out of the way by the rock weighs 7.5 N. The mass of that much water is given by
W = m*g
m = W/g = 7.5 N / (9.8 m/s^2) = 0.765 kg

That bit of information and the density of water can then tell us the volume of the rock.
Density of water = 1000 kg / 1 m^3
Density is mass / volume, so our 0.756 kg has volume given by
Density = 1000 kg/m^3 = 0.765 kg / volume
volume = 0.765 kg / (1000 kg/m^3) = 0.765*10^-3 m^3

With that info, we can find the density of the rock. The rock's mass is
m = W/g = 20 N / 9.8 m/s^2 = 2.04 kg
So density is
density of rock = mass / volume = 2.04 kg / 0.765*10^-3 m^3 = 2670 kg/m^3

Be sure to check my math, I only went thru it once.

(20-12.5)/1 = 20/x
7.5x = 20
x = 20/7.5 = 2.667 kg/dm^3