Physics homework question.. help! (density)?

Question

A block is suspended from a scale and has a weight of 3N. The block is then lowered into a tub of water so that it's completely underwater and the reading on the scale is now 2.43N. Assume that the density of water is 1000 kg/m^3.

What's the density of the block?

Help please? Thanks!

Answer 1

Well, the buoyancy of the block is 3-2.43 N = .57 N (.0581632 kg).  Since the water weighs 1000 kg/m^3 (1 g/cm^3), the block displaces 58.163 cm^3.  And since the block weighs 3 N (306.122 g), it's density is 306.122/58.163 = 5.2632 g/cm^3.

Answer 2

The apparent loss of weight of the block is being caused by what is called the buoyant force. In other words, the buoyant force is 3N - 2.43N = 0.57N

The buoyant force (Fb) = mass of water displaced * g

Which if we multiply the top and bottom by the volume of fluid displaced, V we get

                                 Fb = m * g * V / V

                                 Fb = (rho) * g * V

rho is the density of water.

So now we can calculate the the volume of the block which is the same as the volume of water displaced since it is entirely under water.

                                0.57 = 1000 *  10 * V

                                 V = 5.7 x 10^-5 m^3

The mass can be calculated from the original weight:

weight = mg

3N = m(10)

m = 0.3

density is just m/V

density = 0.3 / 5.7 x 10^-5 m^3

density ~ 5263 kg/m^3

And it should be more dense then water which it is because it sank.

Also i rounded g to 10 to make things easier but if you require more specific calculation then redo it with 9.8