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Exploring Forces - Weight and Its Measurement

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Weight is defined as the force with which an object is attracted towards the center of the Earth or any other celestial body. It is represented by the symbol WW.

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Mass (mm) is the quantity of matter contained in a body and remains constant everywhere in the universe, whereas weight changes depending on the local acceleration due to gravity (gg).

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Weight is a vector quantity because it has both magnitude and a specific direction (towards the center of the planet).

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The SI unit of weight is the Newton (NN), the same as the unit of force. Another common unit used in daily life is the kilogram-force (kgfkgf), where 1 kgf1 \text{ kgf} is the weight of a 1 kg1 \text{ kg} mass.

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The acceleration due to gravity on Earth is approximately g=9.8 m/s2g = 9.8 \text{ m/s}^2. For ease of calculation in some problems, it is often taken as 10 m/s210 \text{ m/s}^2.

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The weight of an object on the Moon is about 16\frac{1}{6} of its weight on Earth because the Moon's gravitational pull is much weaker.

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Weight is measured using a spring balance, which measures the force exerted by the object due to gravity by stretching a calibrated spring.

📐Formulae

W=m×gW = m \times g

gearth≈9.8 m/s2g_{earth} \approx 9.8 \text{ m/s}^2

Wmoon=16×WearthW_{moon} = \frac{1}{6} \times W_{earth}

1 N=1 kg×1 m/s21 \text{ N} = 1 \text{ kg} \times 1 \text{ m/s}^2

💡Examples

Problem 1:

Calculate the weight of an object on Earth if its mass is 50 kg50 \text{ kg}. (Take g=9.8 m/s2g = 9.8 \text{ m/s}^2)

Solution:

Given: m=50 kgm = 50 \text{ kg}, g=9.8 m/s2g = 9.8 \text{ m/s}^2 Using the formula: W=m×gW = m \times g W=50×9.8W = 50 \times 9.8 W=490 NW = 490 \text{ N}

Explanation:

To find the weight, we multiply the mass of the object by the acceleration due to gravity on Earth. The resulting unit is Newtons.

Problem 2:

If an astronaut weighs 600 N600 \text{ N} on Earth, what will be their weight on the Moon?

Solution:

Given: Wearth=600 NW_{earth} = 600 \text{ N} We know that: Wmoon=16×WearthW_{moon} = \frac{1}{6} \times W_{earth} Wmoon=16×600W_{moon} = \frac{1}{6} \times 600 Wmoon=100 NW_{moon} = 100 \text{ N}

Explanation:

Since the Moon's gravity is one-sixth of Earth's gravity, the weight of any object on the Moon is calculated by dividing its weight on Earth by 66.

Problem 3:

An object weighs 20 N20 \text{ N} on Earth. What is its mass? (Take g=10 m/s2g = 10 \text{ m/s}^2)

Solution:

Given: W=20 NW = 20 \text{ N}, g=10 m/s2g = 10 \text{ m/s}^2 Using W=m×gW = m \times g, we can rewrite it as: m=Wgm = \frac{W}{g} m=2010m = \frac{20}{10} m=2 kgm = 2 \text{ kg}

Explanation:

To find the mass when weight is known, we divide the weight by the acceleration due to gravity. Mass is measured in kilograms (kgkg).