Question

consider two cubes: a copper cube (Density = 8.96 g/cm^3) and a lead cube (Density = 11.4 g/cm^3) that both have an edge length of 3.0 cm.

1) which cube (if either) has the greater mass? How do you know?

2) which cube (if either) displaces the more water when fully submerged? how do you know?

3) which cube (if either) experiences the buoyant force of greatest magnidude when fully submerged? How do you know?

4) calculate the magnitude of the buoyant force (in Newtons) acting on the copper cube and the lead cube when each is fully submerged in water. Show your work!

5) If either block is immersed only half-way into the water, how does the magnitude of the bouyant force in this case compare to the buoyant force when that same block is fully submerged? Defend your answer.

Plase show all work. Thank you so much.

Answer 1

1)The Lead cube has greater mass. This is because both the cubes have same volume but the Lead has greater density. For same volume the denser material will be heavier.

2)Both the cubes displace the same amount of water when fully submerged beacause the volumes of displaced water is equal to the volume of cube submerged and in this case both the cubes have same volume.

3)Buoyant force is directly proportional to the density of the material immersed and as both are fully submerged and both have same volume, the lead cube will experience greater buoyant force because of greater density.

4)Buoyant force = d*V*g,where d- density, V- volume, g- gravitational acceleration.

Buoyant force on Lead Cube = 11.4*(0.03*0.03*0.03)*9.8= 3.01644 * 10^(-3)=0.00301 Newtons..

Buoyant force on Copper cCube = 8.96*(0.03*0.03*0.03)*9.8= 2.370816 * 10^(-3)=0.00237 Newtons.

5)When only half submerged the buoyancy force will be halved because the Volume of water displaced will be halved.