Mass, Weight, and Density Practice Answers #

1. a) Weight on Earth:

   Weight = mass × gravitational field strength

   W = 70 kg × 9.81 N/kg = 686.7 N

   b) Weight on Moon:

   W = 70 kg × 1.62 N/kg = 113.4 N

   Answers:

   a) 686.7 N

   b) 113.4 N

   c) Her mass remains 70 kg on the Moon because mass is a measure of the amount of matter in an object and doesn’t depend on gravitational field strength.

2. a) Volume calculation:

   Volume = length × width × height

   Volume = 5 × 4 × 3 = 60 cm³

   b) Density calculation:

   Density = mass ÷ volume

   Density = 120g ÷ 60cm³ = 2 g/cm³

   c) Weight calculation:

   First convert mass to kg: 120g = 0.12 kg

   Weight = 0.12 kg × 9.81 N/kg = 1.18 N

   Answers:

   a) 60 cm³

   b) 2 g/cm³

   c) 1.18 N

3. a) Mass calculation using Earth values:

   Mass = Weight ÷ gravitational field strength

   Mass = 100 N ÷ 9.81 N/kg = 10.2 kg

   To verify using Mars values:

   Mass = 37.2 N ÷ 3.72 N/kg = 10.2 kg

   Answers:

   a) 10.2 kg

   b) The weight is different because gravitational field strength varies between planets, but mass stays the same because it measures the amount of matter in the object, which doesn’t change with location.

4. a) Volume calculation:

   Volume increase = final volume – initial volume

   Volume = 40cm³ – 25cm³ = 15cm³

   b) Density calculation:

   Density = mass ÷ volume

   Density = 35g ÷ 15cm³ = 2.33 g/cm³

   Answers:

   a) 15 cm³

   b) 2.33 g/cm³

   c) The stone will sink because its density (2.33 g/cm³) is greater than the density of water (1 g/cm³). Objects sink in fluids that are less dense than they are.

5. a) Mass calculation:

   Mass = density × volume

   Mass = 2.7 g/cm³ × 8 cm³ = 21.6 g

   b) Weight calculation:

   First convert mass to kg: 21.6 g = 0.0216 kg

   Weight = mass × g = 0.0216 kg × 9.81 N/kg = 0.212 N

   c) Side length calculation:

   Volume of cube = side length³

   8 = side length³

   Side length = ∛8 = 2 cm

   Answers:

   a) 21.6 g

   b) 0.212 N

   c) 2 cm

6. a) Average mass calculation:

   (24.2 + 24.0 + 24.1) ÷ 3 = 24.1 g

   b) Average volume calculation:

   (3.0 + 3.1 + 3.0) ÷ 3 = 3.03 cm³

   c) Density calculation:

   Density = average mass ÷ average volume

   Density = 24.1 g ÷ 3.03 cm³ = 7.95 g/cm³

   Answers:

   a) 24.1 g

   b) 3.03 cm³

   c) 7.95 g/cm³