Question

The gravitational force exerted on a solid object is 5.05 N as measured when the object is suspended from a spring scale as in Figure a. When the suspended object is submerged in water, the scale reads 3.88 N (Figure b). Find the density of the object. Answer is in kg/m^3.

Answer 1

Here are the steps to solve this problem:

Determine the weight of the object in air:

F = ma

Weight (W) = Force (F) x gravitational field strength (g)

W = 5.05 N x 9.8 m/s^2 = 49.5 N

Determine the weight of the object submerged in water:

W' = 3.88 N x 9.8 m/s^2 = 38.0 N

The difference in weight is due to buoyant force:

Fb = Wa - W

Fb = 38.0 N - 49.5 N = 11.5 N

The buoyant force is equal to the weight of the water displaced:

Fb = ρwVg (where ρw is the density of water and V is the volume)

11.5 N = (ρwV)(9.8 m/s^2)

Solve for the volume and density of the object:

V = Fb/( ρwg) = 11.5 N/(1000 kg/m^3)(9.8m/s^2)

= 1.17 x 10^-3 m3

Density of object = mass/volume

ρ = W/V = 49.5 N/(1.17 x 10^-3 m3)

= 4.22 x 104 kg/m3

= 4220 kg/m3

So the density of the object is 4220 kg/m3.

In summary, by using Newton's second law, Archimedes' principle and definitions of weight, buoyant force and density, we were able to determine the density of the object based on measurements in air and water.

Step-by-step explanation: