Question

A ball bearing has mass 0.44 pounds. 1 kg = 2.2 pounds. ​

Answer 1

Answer:

  (i) 0.2 kg

  (ii) kg/cm³

  (b) 2.29 kg

Step-by-step explanation:

This problem gives you relations between units, and the formulas for density and mass. It is asking you to make use of these relations in various mass and density calculations.

(a)(i)

The relationship between kg and pounds can be used to write a units conversion multiplier. It will have numerator equal to denominator, but will have units such that multiplying by it will give the units you want.

  0.44 pounds × multiplier = __ kg

  0.44 pounds × (1 kg)/(2.2 pounds) = (0.44/2.2)(1 kg)

  0.44 pounds = 0.2 kg

__

(a)(ii)

The formula can be used to find the units of interest:

  Density = mass/volume

  units of density = (units of mass)/(units of volume)

  units of density = kg/cm³

__

(b)

Using the given formula with the given value of L, we find the volume to be ...

  V = 4(1.40 cm)(3 -1.40 cm)² = 14.336 cm³

Then the mass is ...

  mass = volume × density

  mass = (14.336 cm³)×(0.160 kg)/(1 cm³) = 2.29376 kg

The mass is about 2.29 kg.

_____

Additional comment

Often you will see density in terms of kg/m³ or g/cm³. Water has a density of about 1 g/cm³ or 1000 kg/m³. The most dense non-radioactive element in the periodic table is osmium, with a density of about 22.6 g/cm³, or 0.0226 kg/cm³. The material in part (b) of this problem has a density about 7 times that, so is clearly not from Earth.