Question

The densities of cork, lead, and water are 0.240, 11.34, and 0.997 g/cm3 at 25°c, respectively. if 20.0 grams of lead are placed inside an 85.0 cm3 piece of cork, what is the overall density and will it float on water?

Answer 1

The overall density of the cork with lead inside is 0.475 g/cm³, which is less than the density of water (0.997 g/cm³). Therefore, it will float on water.

Step-by-step explanation:

To determine the overall density of the composite object of lead and cork and to find out if it will float on water, we first calculate its total mass and total volume. The mass of lead is given as 20.0 grams, and the mass of the cork is found by multiplying the cork's volume (85.0 cm³) by its density (0.240 g/cm³), yielding a mass of 20.4 grams. Adding the two gives a total mass of 40.4 grams. The total volume is the volume of the cork, 85.0 cm³, since the lead is placed inside it and does not add to the volume.

Next, we calculate the overall density using the formula density = mass/volume, which gives us an overall density of 40.4 g / 85.0 cm³ = 0.475 g/cm³. Now, comparing this to the density of water (0.997 g/cm³), we find that the composite object is less dense than water. Since an object will float if its density is less than the fluid's density, the cork with lead inside will float on water.

Answer 2

Answer:

overall density = 0.475 g/cm³
Conclusion: if will float on water


Step-by-step explanation:

1) name the variables:

masa = m
volume = v
density = d

2) Formula

d = m / v ⇒ m = v × d ⇒ v = m / d

3) Solution


i) Calculate the mass of the cork

V cork = 85.0 cm³ ⇒ m = 85.0 cm³ × 0.240 g / cm³ = 20.4 g

ii) Mass of lead + cork

m = 20.0 g + 20.4 g = 40.4 g

iii) Volume of the cork and lead

Assume that, since the lead is inside the cork, the total volume is the same volume of the cork: 85.0 cm³ (any how the contribution of the lead to the volumen is so small that it does not affect the results).


iv) Calculate the overall density

d = 40.4 g / 85.0cm³ = 0.475 g/cm³

4) Conclusion:

Since the overall density is less than the density of water, the object will float.