Question

Density of Planets and Moons Lab

Objectives: In this lab you will learn:

            Part 1 – What density is, and how to experimentally determine it

            Part 2 – To calculate various physical quantities for the planet Mercury

Part 3 – Group major solar system bodies by density

Part 1. DENSITY

Definition – Density =mass / volume.

Symbolically, we write this as

,

where 1) ρ (the Greek letter “rho”) is the density,

             2) m is mass, and

             3) V is volume, the amount of three-dimensional space the object occupies.

The units for density are grams per cubic centimeter, g/cm³.

Since this experiment will only consider spherical objects (planets and major moons), we need to know how to calculate the volume of a sphere, which is given by the equation

where 1) V is the volume of the sphere, and

             2)  r is the radius of the sphere.

From the equation, we see that our only value containing units is the radius, which is distance.  Since we are cubing it, our answer for volume should always have units of distance cubed.  Since volume is three dimensional, this always the case for the volume in any object, not just spheres.

We will begin by finding the density of three small, spherical objects.  Follow the procedure to measure the values.

Procedure – Use your data from Lab 5 to fill in this table. Then use your data to answer the questions.

Table 1.

Ball	Mass (g)	Diameter (mm)	Radius (mm)	Radius (cm)
Golf Ball	43.9 g	41.74 mm	20.87 mm	2.087 cm
Steel Ball	27.9 g	19.06 mm	9.53 mm	.953 cm
Ping Pong Ball	2.5 g	39.45 mm	19.725 mm	1.9725 cm

• 1. Calculate the density of the golf ball.  Show your work.

• 2. Calculate the density of the steel ball.  Show your work.

• 3. Calculate the density of the ping pong ball.  Show your work

4. If two spheres have the same mass and different radii, which will be more dense, and why?

5. If two spheres have the same radius and different masses, which one will be more dense, and why?

6. (5 points)  Would it always be true that a sphere with a smaller diameter would be denser, and why or why not?

7. (5 points)  Would it always be true that a sphere with a greater mass would be denser, and why or why not?

8. (5 points)  If all of the balls had exactly the same mass, which would be the densest, and why?

Part 2. MERCURY

Consider Mercury’s mass.  Since we are studying comparative planetology, we often give the mass of planets as multiples of Earth’s mass.  But if we want to calculate a planet’s (observed) density, then we need its mass in grams.

• 9. (5 points) The mass of Mercury is 0.055 times Earth’s mass.  Earth’s mass, in kilograms, is 5.9722 × 10²⁴kg.  Calculate Mercury’s mass in kilograms.  Show your work.

• 10. (5 points) The metric prefix kilo means 1,000, so 1 kilogram = 1,000 grams.  Convert Mercury’s mass in kilograms into mass in grams.  (HINT: 1,000 = 10³, and if the unit is smaller, the number must be correspondingly bigger.  By the law of exponents,

10^a ∙ 10^b = 10^a+b.)  Show your work.

Now we will consider Mercury’s radius.  We wish to calculate density, so we need to convert Mercury’s radius into centimeters.  As an intermediate step, we will first find Mercury’s radius in meters.

• 11. (5 points) Mercury’s radius is 2,440 km.  1 km = 1,000 m.  Convert Mercury’s radius into meters.  Show your work.

• 12. The metric prefix centi means 1/100, i.e. 0.01, which can also be expressed as 10^-2.  Thus, 1 m = 100 cm.  Convert Mercury’s radius into centimeters.  Show your work.

• 13.  Using the equation for the volume of a sphere, calculate Mercury’s volume, in cubic centimeters.

• 14. Calculate the density of Mercury, in grams per cubic centimeter.  Show your work.

• 15. A typical range of density values for common rocks is 2.0 – 3.0 g/cm³, and a typical range for metals is 7 - 20 g/cm³.  Based on your answer to 17, how would you describe Mercury’s composition, in terms of materials?

Answer 1