Mass, Weight, and Gravity: Complete Answer Key for 3rd Grade

Master the relationship between mass, weight, and gravity with these 5 detailed exercises including comprehensive explanations, rules, and visual learning aids.

Answer Key: Exercises 1 to 3
1 Gravity Effects on Weight
Exercise 1
A cat has a mass of 4 kg on Earth. What would its mass and weight be on the Moon? (Gravity on Moon is 1/6th of Earth's gravity). Explain why mass stays the same but weight changes.
Key Definitions:

Mass: The amount of matter in an object. Measured in grams (g) or kilograms (kg). Stays the same everywhere in the universe.

Weight: The force of gravity acting on an object. Measured in grams (on Earth) or Newtons. Changes depending on the strength of gravity.

Gravity: The force that pulls objects toward a planet or moon. Different celestial bodies have different gravitational strengths.

Method:
  1. Remember: Mass is constant, weight is variable based on gravity
  2. Calculate weight using gravitational ratio
  3. Explain the physics behind the difference
Object
Cat
Earth Mass
4 kg
Moon Mass
4 kg
Step 1: Identify the mass

The cat's mass is 4 kg. This does NOT change regardless of location.

Step 2: Calculate weight on Earth

Weight on Earth = 4 kg (as measured by scale)

Step 3: Calculate weight on Moon

Weight on Moon = Weight on Earth × (1/6)

Weight on Moon = 4 kg × (1/6) ≈ 0.67 kg

Step 4: Explain the physics

Mass stays the same because it measures the amount of matter in the cat.

Weight changes because gravity is weaker on the Moon, so there's less force pulling the cat down.

Mass = 4 kg (constant), Weight on Moon ≈ 0.67 kg
Final answer:

The cat's mass remains 4 kg on the Moon, but its weight would be approximately 0.67 kg because the Moon's gravity is only 1/6th of Earth's gravity.

Applied rules:

• Mass Constant: Mass does not change with location

• Weight Variable: Weight depends on gravitational force

• Moon Gravity: About 1/6th of Earth's gravity

2 Comparing Weight on Different Planets
Exercise 2
A bag of sugar has a mass of 2 kg. Compare its weight on Earth, Moon, and Jupiter. (Gravity ratios: Moon = 1/6 of Earth, Jupiter = 2.4 times Earth's gravity)
Definition:

Gravitational Effect: Different planets have different gravitational strengths, affecting weight while mass remains constant.

Object
Sugar Bag
Mass
2 kg
Weights
E: 2kg, M: 0.33kg, J: 4.8kg
Step 1: Establish the constant

Mass = 2 kg (stays the same everywhere)

Step 2: Calculate weight on Earth

Weight on Earth = 2 kg (standard measurement)

Step 3: Calculate weight on Moon

Weight on Moon = 2 kg × (1/6) = 0.33 kg

Step 4: Calculate weight on Jupiter

Weight on Jupiter = 2 kg × 2.4 = 4.8 kg

Step 5: Compare results

Jupiter > Earth > Moon in terms of weight

Earth: 2kg, Moon: 0.33kg, Jupiter: 4.8kg
Final answer:

The sugar bag has the same mass (2 kg) everywhere, but its weight varies: 2 kg on Earth, 0.33 kg on the Moon, and 4.8 kg on Jupiter.

Applied rules:

• Mass Constant: Mass remains unchanged

• Weight Proportional: Weight changes proportionally with gravity

• Planet Comparison: Stronger gravity = heavier weight

3 Calculating Gravitational Effects
Exercise 3
A child has a mass of 30 kg on Earth. If the child travels to Mars where gravity is 0.38 times Earth's gravity, what would be the child's weight on Mars? If the child brought a 1 kg toy, what would be the toy's weight on Mars?
Definition:

Gravitational Calculation: Weight = Mass × Gravitational Factor. Mass remains constant while weight varies.

Child
30 kg
Mars Gravity
0.38 × Earth
Mars Weight
11.4 kg
Step 1: Calculate child's weight on Mars

Weight on Mars = Mass × Gravitational factor

Weight on Mars = 30 kg × 0.38 = 11.4 kg

Step 2: Calculate toy's weight on Mars

Weight on Mars = Mass × Gravitational factor

Weight on Mars = 1 kg × 0.38 = 0.38 kg

Step 3: Analyze the pattern

Both objects lose weight proportionally to Mars' gravity

Everything becomes 38% of its Earth weight

Step 4: Verify calculations

Child: 30 kg × 0.38 = 11.4 kg ✓

Toy: 1 kg × 0.38 = 0.38 kg ✓

Child: 11.4 kg, Toy: 0.38 kg
Final answer:

The child would weigh 11.4 kg on Mars and the toy would weigh 0.38 kg on Mars. Both objects maintain their mass but experience reduced weight due to Mars' weaker gravity.

Applied rules:

• Formula: Weight = Mass × Gravity Factor

• Proportional Reduction: Weight decreases proportionally

• Mass Conservation: Mass remains unchanged

Mass, Weight, and Gravity Relationships
Weight = Mass × Gravity
Core Formula
Mass
Constant Everywhere
Amount of matter
Weight
Variable with Gravity
Force of attraction
Gravity
Planet-Specific
Force multiplier
Key Concepts:

Mass: Amount of matter in an object (measured in g/kg)

Weight: Force due to gravity (affected by location)

Gravity: Force that pulls objects toward planetary bodies

Calculation Techniques:
  1. Identify Constants: Mass always remains the same
  2. Determine Gravity Factor: Compare to Earth's gravity
  3. Apply Formula: Weight = Mass × Gravity Factor
  4. Verify Results: Check if answer makes sense
Tip 1: Mass is "what you're made of", weight is "how heavy you feel".
Tip 2: Stronger gravity = heavier weight, weaker gravity = lighter weight.
Tip 3: Always multiply mass by gravity factor to find weight.
Tip 4: Remember: 1 kg on Earth ≠ 1 kg on other planets (weight changes).
Common Mistake: Thinking mass and weight are the same everywhere.
Memory Aid: "Mass" = "Matter" (always the same).
Essential Rules:

• Mass is always constant regardless of location

• Weight varies with gravitational pull

• Weight = Mass × Gravity Factor

• Different planets have different gravity strengths

Answer Key: Exercises 4 to 5
4 Gravity Comparison Analysis
Exercise 4
A rock has a mass of 5 kg on Earth. If the same rock were taken to Venus (gravity = 0.91 times Earth's gravity) and Neptune (gravity = 1.14 times Earth's gravity), calculate its weight on each planet. Which planet would make the rock feel heaviest?
Definition:

Planetary Gravity Comparison: Calculating weight differences across various planetary bodies using their gravitational factors.

Object
Rock
Mass
5 kg
Results
V: 4.55kg, N: 5.7kg
Step 1: Calculate weight on Venus

Weight on Venus = Mass × Venus Gravity Factor

Weight on Venus = 5 kg × 0.91 = 4.55 kg

Step 2: Calculate weight on Neptune

Weight on Neptune = Mass × Neptune Gravity Factor

Weight on Neptune = 5 kg × 1.14 = 5.7 kg

Step 3: Compare weights

Neptune: 5.7 kg > Earth: 5 kg > Venus: 4.55 kg

Step 4: Identify heaviest planet

Neptune has the strongest gravity among the three, making the rock heaviest

Step 5: Verify calculations

Venus: 5 × 0.91 = 4.55 kg ✓

Neptune: 5 × 1.14 = 5.7 kg ✓

Venus: 4.55 kg, Neptune: 5.7 kg, Neptune is heaviest
Final answer:

The rock would weigh 4.55 kg on Venus and 5.7 kg on Neptune. The rock would feel heaviest on Neptune because it has the strongest gravitational pull among the three locations.

Applied rules:

• Weight Formula: Weight = Mass × Gravity Factor

• Comparison: Higher gravity = higher weight

• Mass Conservation: Mass remains 5 kg everywhere

5 Gravity-Weight Relationship Problem
Exercise 5
A scientist measures an object's weight on three different planets. On Planet X, the object weighs 12 kg. On Planet Y, it weighs 6 kg. On Planet Z, it weighs 24 kg. If the object's mass is 8 kg, calculate the gravity factor for each planet compared to Earth. Which planet has the strongest gravity?
Definition:

Gravity Factor Calculation: Using the formula Weight = Mass × Gravity Factor, rearrange to find Gravity Factor = Weight ÷ Mass.

Given
Mass = 8 kg
Weights
X: 12kg, Y: 6kg, Z: 24kg
Factors
X: 1.5, Y: 0.75, Z: 3.0
Step 1: Recall the formula

Weight = Mass × Gravity Factor

Therefore: Gravity Factor = Weight ÷ Mass

Step 2: Calculate Planet X's gravity factor

Gravity Factor X = 12 kg ÷ 8 kg = 1.5

Planet X has 1.5 times Earth's gravity

Step 3: Calculate Planet Y's gravity factor

Gravity Factor Y = 6 kg ÷ 8 kg = 0.75

Planet Y has 0.75 times Earth's gravity

Step 4: Calculate Planet Z's gravity factor

Gravity Factor Z = 24 kg ÷ 8 kg = 3.0

Planet Z has 3 times Earth's gravity

Step 5: Compare and identify strongest

Planet Z (3.0) > Planet X (1.5) > Earth (1.0) > Planet Y (0.75)

Planet Z has the strongest gravity

X: 1.5×, Y: 0.75×, Z: 3.0×, Planet Z strongest
Final answer:

Planet X has 1.5 times Earth's gravity, Planet Y has 0.75 times Earth's gravity, and Planet Z has 3 times Earth's gravity. Planet Z has the strongest gravity, making objects weigh three times as much as on Earth.

Applied rules:

• Rearranged Formula: Gravity Factor = Weight ÷ Mass

• Proportional Reasoning: Calculate ratios to Earth

• Comparison Analysis: Identify strongest gravitational field

Comprehensive Mass, Weight, and Gravity Summary
Weight = Mass × Gravity
Fundamental Relationship
Key definitions:

Mass: Amount of matter in an object (constant, measured in g/kg)

Weight: Force of gravity on an object (variable, depends on location)

Gravity: Force that pulls objects toward planetary bodies

Complete methodology:
  1. Identify constants: Determine what stays the same (mass)
  2. Determine variables: Identify what changes (gravity, weight)
  3. Apply formula: Use Weight = Mass × Gravity Factor
  4. Verify results: Check if answer makes logical sense
Tip 1: Think of mass as "amount of stuff" and weight as "how heavy it feels".
Tip 2: Stronger gravity = heavier weight, weaker gravity = lighter weight.
Tip 3: Balance scales measure mass directly, bathroom scales measure weight.
Tip 4: Always write the unit (g or kg) with your answer.
Common errors: Mixing up mass and weight, forgetting units, incorrect conversions.
Key memorization: Mass is constant, weight varies with gravity.
Essential rules to remember:

• Mass remains constant everywhere in the universe

• Weight changes depending on gravitational force

• Weight = Mass × Gravity Factor

• Different planets have different gravity strengths

• Always include units in your final answer

Questions & Answers

Question: If I weigh myself on Earth and then on the Moon, would I really weigh less? But I would still be me, right? I'm confused about how I can be the same person but weigh differently.

Answer: That's a great observation! You're absolutely right - you would still be the same person, just experiencing different gravity:

  • Your mass (the amount of matter in your body) stays exactly the same
  • Your weight (how hard gravity pulls on you) changes because the Moon's gravity is weaker

Think of it like this: You're made of the same number of atoms whether you're on Earth or the Moon. But on the Moon, those atoms are being pulled down with less force, so you feel lighter. Your body hasn't changed, but the force acting on it has!

It's like having the same amount of clay but pressing it gently vs. pressing it hard - the clay is the same, but the pressure is different.

Question: How do scientists know how strong gravity is on other planets? Is there a special way to measure it?

Answer: Scientists use several clever methods to determine gravity on other planets:

  • Observation: Watch how moons orbit the planet or how objects fall
  • Math: Use the planet's size and mass to calculate gravity
  • Spacecraft: Send probes that can measure gravitational pull directly

For example, if they see a moon moving slowly around a planet, they know the gravity is stronger. If they send a probe and see how fast it falls, they can calculate exactly how strong the gravity is!

The bigger and denser a planet, the stronger its gravity. That's why Jupiter has much stronger gravity than Earth.

Question: If I could live on Jupiter, would I be able to jump as high as on Earth? Would everything feel super heavy?

Answer: On Jupiter, you would face some amazing challenges:

  • You would weigh about 2.4 times more than on Earth!
  • Jumping would be extremely difficult - you might barely lift off the ground
  • Everything would feel much heavier
  • Walking would require much more effort

If you weigh 30 kg on Earth, you would feel like you weigh about 72 kg on Jupiter! Your muscles would have to work much harder to move your body.

That's why astronauts training for missions practice in different conditions to prepare for varying gravity levels.