Physics 101 word problem

Question

A standard baseball has a circumference of approxi- mately 23 cm. If a baseball had the same mass per unit volume as a neutron or a proton, about what would its mass be?

Answer 1

The first step is to find the density of proton or neutron from a reputable source. (Wikipedia’s 10¹⁸ kg/m³ is a very rough estimate, it is an order of magnitude rather than a value to be used in calculations.)

NASA’s website gives the density of neutron to be equal to 3.0 × 10²⁷ kg/km³

heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/ns.html

The next step is to convert the density to kg/cm³

1 km = 1 × 10⁵ cm, therefore 1 km³ = 1 × 10¹⁵ cm³ and

3.0 × 10²⁷ kg/km³ = 3.0 × 10¹² kg/cm³

Next we need to find the volume V of the ball given its circumference C

We know that C = 2πR, which means that R = C/2π,

and that V = 4πR³/3

Substituting R = C/(2π) we get

V = 4π(C/2π)³/3 = C³ /(6π²) = 23³ /(6π²) cm³ = 205 cm³

Finally we can convert volume to mass using density as a conversion factor.

205 cm³ × 3.0 × 10¹² kg/cm³ = 6.2 × 10¹⁴ kg

(We only keep 2 significant figures, because both 23 cm and 3.0 × 10²⁷ kg/km³ have 2 significant figures)

Answer 2