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define-g-on-earths-surface

🚀 Gravitation is a fundamental force of nature that attracts two bodies towards each other. The acceleration due to gravity, denoted as 'g', is the acceleration experienced by an object due to the gravitational pull of the Earth. On the surface of the Earth, this value is approximately 9.81 m/s². This means that any object falling freely under the influence of gravity will increase its velocity by about 9.81 meters per second for every second it falls. The value of 'g' can vary slightly depending on altitude and geographical location, but for most calculations, we use the standard value of 9.81 m/s².

Theory Explanation

Understanding Gravitational Force

The gravitational force between two masses is given by Newton's law of universal gravitation, which states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

\[ F = G \frac{m_1 m_2}{r^2} \]
Calculating Acceleration Due to Gravity

To find the acceleration due to gravity at the surface of the Earth, we can use the formula derived from Newton's law of gravitation. The mass of the Earth (M) and the radius of the Earth (R) are used in the formula: g = G * M / R², where G is the gravitational constant (6.674 × 10⁻¹¹ N(m/kg)²).

\[ g = G \frac{M}{R^2} \]

Key Points

  • 🎯 Gravitation is a universal force that acts between all masses.
  • 🎯 The acceleration due to gravity on Earth is approximately 9.81 m/s².
  • 🎯 The value of 'g' can vary slightly based on altitude and location.
  • 🎯 Gravitational force decreases with distance from the Earth's center.
  • 🎯 The formula for gravitational force is F = G * (m1 * m2) / r².

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Examples:💡

Calculate the weight of a 10 kg object on the surface of the Earth.

Solution:

Step 1: Use the formula for weight, W = m * g, where m is the mass and g is the acceleration due to gravity.

\[ W = 10 \text{ kg} \times 9.81 \text{ m/s}^2 \]

Step 2: Calculate W = 10 * 9.81 = 98.1 N.

\[ W = 98.1 \text{ N} \]

An object is dropped from a height of 20 meters. Calculate the time it takes to reach the ground.

Solution:

Step 1: Use the formula for free fall: h = 0.5 * g * t², where h is the height, g is the acceleration due to gravity, and t is the time.

\[ 20 = 0.5 \times 9.81 \times t^2 \]

Step 2: Rearranging gives t² = (20 * 2) / 9.81.

\[ t^2 = \frac{40}{9.81} \]

Step 3: Calculate t = √(40/9.81) ≈ 2.02 seconds.

\[ t \approx 2.02 \text{ seconds \]

Common Mistakes

  • Mistake: Confusing weight with mass; weight is dependent on gravity while mass is constant.

    Correction: Always remember that weight is the force due to gravity acting on a mass, calculated as W = m * g.

  • Mistake: Neglecting the effect of air resistance in free fall problems.

    Correction: In introductory physics, we often ignore air resistance unless specified; however, in real scenarios, it can affect the fall time.

  • Mistake: Using incorrect values for g in calculations; sometimes students use 10 m/s² instead of 9.81 m/s².

    Correction: Always use the precise value of g = 9.81 m/s² unless otherwise instructed.

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