Unit 5.4 – Mass & Weight

• Units of Mass: The SI unit of mass is the kilogram (kg).
• Key Point: Mass is constant everywhere—on Earth, the Moon, or in space.

• Formula for Weight:

• $𝑊$: Weight (in Newtons, N)
• $𝑚$: Mass of the object (in kilograms, kg)
• $𝑔$: Acceleration due to gravity ($9.8{\text{m/s}}^2$ on Earth)
• Key Point: Weight changes depending on the value of $𝑔$. For example, your weight on the Moon is about $\frac{1}{6}$ of your weight on Earth because the Moon’s $𝑔$ is smaller.

Key Points About Mass and Weight

1. Difference Between Mass and Weight:
   • Mass: A measure of the amount of matter in an object. It is constant everywhere.
   • Weight: A measure of the gravitational force acting on the object. It varies with location.
2. Units:
   • Mass is measured in kilograms (kg).
   • Weight is measured in Newtons (N).
3. Effect of Gravity:
   • On Earth: $𝑔=9.8{\text{m/s}}^2$, so weight is calculated as $𝑊=𝑚\cdot 9.8$.
   • On the Moon: $𝑔=1.6{\text{m/s}}^2$, so weight is much smaller.
4. Real-Life Example:
   • An astronaut with a mass of $70\text{kg}$ weighs $686\text{N}$ on Earth ($𝑊=70\cdot 9.8$) but only $112\text{N}$ on the Moon ($𝑊=70\cdot 1.6$).

Detailed Notes with Bullets

1. Why Does Weight Change but Mass Stays Constant?

• Mass:
  • Mass is the amount of matter in an object. It doesn’t depend on gravity.
  • Example: A $10\text{kg}$ bag of rice has the same mass on Earth, the Moon, or in space.
• Weight:
  • Weight depends on gravity. If gravity changes, weight changes.
  • Example: The same $10\text{kg}$ bag weighs $98\text{N}$ on Earth but only $16\text{N}$ on the Moon.

2. How to Calculate Weight

• Use the formula:

• A $50\text{kg}$ person on Earth:

• The same person on the Moon:

3. What Happens in Space?

• In space, far away from any planet or star, there is no significant gravity.
• Objects are weightless, but their mass remains unchanged.
• Example: Astronauts in the International Space Station (ISS) float because they are in free fall, but their mass is still the same as on Earth.

4. Common Misconceptions

• People often confuse mass and weight because we use scales to measure weight in everyday life.
  • Scales actually measure the force (weight) caused by gravity, but they display it in units like kilograms for convenience.

Quick Review, Exam Tips, Tricks & Traps

Key Points to Remember

• Mass is constant; weight depends on gravity.
• Use $𝑊=𝑚\cdot 𝑔$ to calculate weight.
• Weight changes with location, but mass does not.

Exam Tips

1. Always check if the question asks for mass or weight.
   • Mass is in kilograms ($\text{kg}$); weight is in Newtons ($\text{N}$).
2. Use the correct value of $𝑔$:
   • $𝑔=9.8{\text{m/s}}^2$ on Earth.
   • $𝑔=1.6{\text{m/s}}^2$ on the Moon.
3. Remember that weightlessness in space means no gravity, but mass is still present.

Common Traps

1. Students often confuse mass and weight.
   • Mass is constant; weight changes with gravity.
2. Misinterpreting scales: Scales measure weight but display it in kilograms for convenience.

Tricks for Competitive Exams

1. Look for keywords like "mass," "weight," or "gravity" to identify what is being asked.
2. In MCQs, eliminate options where mass changes—it’s impossible unless the object loses or gains matter.
3. Use proportional reasoning:
   • If $𝑔$ decreases, weight decreases proportionally.

Quick Recall Table

Additional Content: Real-Life Examples and Applications

1. Everyday Scales

• Bathroom scales measure weight but display it in kilograms for convenience.
• Example: A scale showing $60\text{kg}$ actually measures a weight of $588\text{N}$ ($60\cdot 9.8$).

2. Astronaut Training

• Astronauts experience weightlessness during training to simulate conditions in space.
• Their mass remains the same, but they feel weightless because there is no gravity acting on them.

3. Planetary Exploration

• Rovers sent to Mars are designed to handle the lower gravity ($𝑔=3.7{\text{m/s}}^2$).
• Example: A $200\text{kg}$ rover weighs $1960\text{N}$ on Earth but only $740\text{N}$ on Mars.

4. Sports and Gravity

• Athletes perform differently on planets with different gravity.
• Example: Jumping on the Moon would be easier because of the lower gravity.