Solved Exercises on Measuring Weight vs Mass in Grade 2

Master measuring weight vs mass: understanding differences, comparing measurements, solving problems with units through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Understanding Weight vs Mass
Exercise 1
Tom's toy car has a mass of 5 kg on Earth. What happens to its mass and weight on the Moon?
🌎
Weight: 5 kg
🚗
Earth
→
🌕
Weight: 0.8 kg
🚗
Moon
🌎
Mass: 5 kg
🚗
Earth
→
🌕
Mass: 5 kg
🚗
Moon
Definition:

Mass: How much matter (stuff) is in an object. It stays the same everywhere.

Weight: How heavy something feels because of gravity. It changes depending on where you are.

Understanding the difference:
  1. Mass: Always stays the same, no matter where you go
  2. Weight: Changes depending on the pull of gravity
  3. On the Moon, gravity pulls less strongly, so things weigh less
  4. But the amount of matter (mass) doesn't change
Step 1: Identify the mass on Earth

The toy car's mass is 5 kg on Earth. This doesn't change.

Step 2: Understand what happens to weight

On the Moon, the same car feels lighter because gravity is weaker.

Step 3: State the results

Mass stays 5 kg, but weight becomes 0.8 kg on the Moon.

Mass: 5 kg (same everywhere) | Weight: 5 kg on Earth, 0.8 kg on Moon
Final answer:

The toy car's mass stays 5 kg, but its weight changes from 5 kg on Earth to 0.8 kg on the Moon.

Applied rules:

• Mass is constant: The amount of matter in an object never changes

• Weight varies: Weight depends on gravity, which differs by location

• Gravity effect: The Moon's gravity is about 1/6 of Earth's gravity

2 Comparing Weight and Mass
Exercise 2
Which statement is true about a 10 kg backpack?
A) Its mass is 10 kg on Earth and 10 kg on the Moon
B) Its weight is 10 kg on Earth and 10 kg on the Moon
C) Its mass changes when moved from Earth to Moon
🎒
10 kg
Backpack
VS
🎒
10 kg
on Moon?
Definition:

Constant Property: Mass remains unchanged regardless of location.

Variable Property: Weight changes based on gravitational force.

Step 1: Analyze option A

Mass is always constant. A 10 kg backpack has 10 kg mass on Earth AND on the Moon.

Step 2: Analyze option B

Weight changes with location. The same backpack weighs less on the Moon.

Step 3: Analyze option C

Mass never changes. The amount of matter in the backpack stays the same.

Step 4: Select the correct answer

Option A is correct because mass remains constant.

A) Its mass is 10 kg on Earth and 10 kg on the Moon
Final answer:

The correct answer is A: The backpack's mass is 10 kg on both Earth and the Moon.

Applied rules:

• Mass constancy: Mass is always the same regardless of location

• Weight variability: Weight changes with gravitational pull

• Analysis: Carefully evaluate each option against known facts

3 Calculating Total Weight
Exercise 3
Sarah has 3 books. Book 1 has a mass of 1 kg, Book 2 has a mass of 2 kg, and Book 3 has a mass of 3 kg. What is their total mass and weight on Earth?
📚
1 kg
Book 1
+
📚
2 kg
Book 2
+
📚
3 kg
Book 3
=
❓
? kg
Total
Definition:

Total Mass: The sum of all individual masses. On Earth, weight equals mass in kg.

Step 1: Identify individual masses

Book 1 = 1 kg, Book 2 = 2 kg, Book 3 = 3 kg

Step 2: Add the masses together

1 kg + 2 kg + 3 kg = 6 kg

Step 3: Determine the relationship on Earth

On Earth, the weight in kg equals the mass in kg

Step 4: State the total

Total mass = 6 kg, Total weight = 6 kg on Earth

Total mass = 6 kg, Total weight = 6 kg on Earth
Final answer:

The total mass of all books is 6 kilograms, and their total weight on Earth is also 6 kilograms.

Applied rules:

• Addition: To find total mass, add all individual masses

• Earth equivalence: On Earth, weight in kg equals mass in kg

• Consistency: Mass remains the same regardless of location

Weight vs Mass: Complete Guide
Mass \space (constant) \neq Weight \space (variable)
Weight vs Mass Formula
Mass
Amount \space of \space Matter
Stays the same everywhere
Weight
Effect \space of \space Gravity
Changes with location
Earth Relationship
Weight = Mass
On Earth, same numbers
Key definitions:

Mass: The amount of matter in an object. Measured in kilograms (kg) or grams (g). Does not change.

Weight: How heavy something feels due to gravity. Also measured in kg or g, but can change depending on location.

Gravity: The force that pulls objects toward each other. Stronger on Earth than on the Moon.

Complete methodology:
  1. Identify the concept: Determine if the problem is about mass or weight
  2. Consider location: Note whether the object is on Earth or elsewhere
  3. Apply the principle: Remember mass is constant, weight varies
  4. Calculate if needed: Add or compare values as required
Tip 1: Remember: Your mass stays the same, but your weight would be less on the Moon!
Tip 2: On Earth, we often use kg for both mass and weight. In science, they're different!
Tip 3: Think of mass as how much "stuff" is in something, weight as how heavy it feels.
Common errors: Thinking mass and weight are the same thing, forgetting that weight changes with location.
Key concept: Mass is constant, weight depends on gravity. On Earth, they have the same numerical value.
Important rules to remember:

• Mass constancy: Mass never changes, no matter where you go

• Weight variability: Weight changes based on gravitational force

• Earth equivalence: On Earth, weight in kg equals mass in kg

• Units: Both are measured in kg or g

Solution: Exercises 4 to 5
4 Finding Missing Values
Exercise 4
A box has a mass of 12 kg on Earth. If you remove 4 kg of items, what is the new mass and weight on Earth?
📦
12 kg
Original
-
🗑️
4 kg
Removed
=
❓
? kg
New
Definition:

Change in Mass: When material is added or removed, mass changes. Weight changes proportionally.

Step 1: Identify the original mass

The box originally has a mass of 12 kg

Step 2: Identify the mass removed

4 kg of items are removed from the box

Step 3: Calculate the new mass

New mass = Original mass - Removed mass = 12 kg - 4 kg = 8 kg

Step 4: Determine the new weight on Earth

On Earth, weight equals mass, so the new weight is also 8 kg

New mass = 8 kg, New weight = 8 kg on Earth
Final answer:

The new mass is 8 kilograms, and the new weight on Earth is also 8 kilograms.

Applied rules:

• Mass change: When matter is removed, mass decreases by the same amount

• Weight correlation: On Earth, weight changes proportionally to mass

• Subtraction: To find remaining mass, subtract the removed amount

5 Real World Application
Exercise 5
An astronaut has a mass of 70 kg on Earth. What would happen to their mass and weight on the Moon? Why might this be important for space travel?
🌎
Weight: 70 kg
👨‍🚀
Earth
→
🌕
Weight: 11.7 kg
👨‍🚀
Moon
🌎
Mass: 70 kg
👨‍🚀
Earth
→
🌕
Mass: 70 kg
👨‍🚀
Moon
Definition:

Real-world Application: Understanding mass vs weight helps in engineering, space travel, and daily life applications.

Step 1: Identify the astronaut's mass on Earth

The astronaut has a mass of 70 kg on Earth

Step 2: Determine the astronaut's mass on the Moon

Mass stays the same: 70 kg on the Moon

Step 3: Determine the astronaut's weight on the Moon

Weight decreases: 70 kg ÷ 6 ≈ 11.7 kg on the Moon

Step 4: Explain the importance for space travel

This knowledge helps engineers design equipment that works in different gravity conditions

Mass: 70 kg (same everywhere) | Weight: 70 kg on Earth, 11.7 kg on Moon
Final answer:

The astronaut's mass remains 70 kg on both Earth and the Moon, but their weight changes from 70 kg on Earth to approximately 11.7 kg on the Moon. This is important for space travel because:

  • Spacecraft must be designed to work in different gravitational environments
  • Tools and equipment need to function properly in lower gravity
  • Astronauts need to adapt to the feeling of being lighter
Applied rules:

• Mass constancy: The astronaut's mass remains 70 kg regardless of location

• Weight calculation: Moon's weight ≈ Earth's weight ÷ 6

• Practical application: Understanding these concepts is crucial for real-world scenarios

Complete Summary: Weight vs Mass
Mass \space (constant) \neq Weight \space (variable)
Weight vs Mass Formula
Key definitions:

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

Weight: The force of gravity acting on an object. Measured in Newtons in physics, but commonly expressed in kg for simplicity. Changes depending on the gravitational field.

Gravity: The natural force that attracts objects with mass toward each other. Stronger on massive planets like Earth, weaker on smaller bodies like the Moon.

Complete methodology:
  1. Distinguish concepts: Always identify whether a problem relates to mass or weight
  2. Consider context: Note the location (Earth, Moon, etc.) for weight calculations
  3. Apply principles: Remember mass is constant, weight varies with gravity
  4. Calculate accurately: Perform operations while keeping units consistent
  5. Verify results: Check if the answer makes logical sense
Tip 1: Remember: Your mass is the same on Earth and the Moon, but you'd weigh less on the Moon.
Tip 2: Think of mass as how much "stuff" is in something, weight as how heavy it feels.
Tip 3: On Earth, we often use kg for both mass and weight, but scientifically they are different.
Tip 4: A scale measures weight, but on Earth it shows mass because of the relationship between them.
Common errors: Confusing mass with weight, forgetting that weight changes with location, mixing up units.
Key concept: Mass is an intrinsic property that never changes, weight is an extrinsic property that varies with gravity.
Essential formulas and rules:

• Mass constancy: Mass remains unchanged regardless of location (m_Earth = m_Moon)

• Weight variation: Weight changes with gravitational force (W = m × g)

• Earth equivalence: On Earth's surface, weight in kg numerically equals mass in kg

• Moon relationship: Weight on Moon ≈ 1/6 × Weight on Earth

• Unit consistency: Always use the same units when comparing or calculating

Questions & Answers

Question: I still don't understand why mass stays the same but weight changes. Can you explain it more simply?

Answer: Great question! Think of it this way:

  • Mass is like the amount of "stuff" in something - imagine building a tower with 10 blocks. No matter where you take those blocks (to school, home, the Moon), you still have 10 blocks!
  • Weight is how heavy something feels - imagine holding a balloon. On Earth, gravity pulls it down and it feels light. But if you went somewhere with weaker gravity (like the Moon), it would feel even lighter!

So the amount of "stuff" (mass) never changes, but how heavy it feels (weight) depends on where you are and how strong gravity is pulling.

Example: If you have a 5 kg backpack, it contains the same amount of material whether you're on Earth or the Moon. But on the Moon, it would feel much lighter because the Moon's gravity isn't pulling as hard.

Question: When I step on a scale, am I measuring my mass or my weight? And why does the number change if I go to the Moon?

Answer: This is a bit tricky! Here's what happens:

  • What a scale measures: Technically, a scale measures weight (the force of gravity pulling on you)
  • How it displays: On Earth, scales are calibrated to show your mass in kg because on Earth, weight and mass have the same numerical value
  • On the Moon: If you took the same scale to the Moon, it would show a smaller number because gravity is weaker there

So when you see "50 kg" on a scale on Earth, you're seeing your mass. But the scale is actually measuring how hard gravity is pulling on you (your weight), then converting that to the equivalent mass.

If you took the scale to the Moon, it would show about 8.3 kg because the Moon's gravity is about 1/6th of Earth's gravity. But your actual mass would still be 50 kg!

Question: If I have a 10 kg dog, how much would it weigh on the Moon? Would it still be 10 kg?

Answer: This is a great example to understand the difference! Let's break it down:

  • Mass: Your dog's mass would stay 10 kg on both Earth and the Moon. The amount of "dog stuff" doesn't change!
  • Weight: Your dog's weight would be different on the Moon. Since the Moon's gravity is about 1/6th of Earth's gravity, your dog would weigh about 1.7 kg on the Moon

So yes, your dog would still have a mass of 10 kg on the Moon, but it would weigh only about 1.7 kg. This means your dog would feel much lighter on the Moon and could jump higher!

The calculation: 10 kg (Earth weight) ÷ 6 = approximately 1.7 kg (Moon weight)

Remember: Mass stays the same, weight changes with gravity!