Gravitational Force Calculations

Gravitational Force

Gravitational Force Between Two Objects

• The problem aims to find the gravitational force ($f_g$) between two masses.
• Given:
  • Mass 1 ($m_1$) = 70 kg
  • Mass 2 ($m_2$) = 52 kg
  • Distance (r) = 1.5 meters
  • Gravitational constant ($G$) = $6.67 \, x \, 10^{-11}$
• Formula:
  • $F<em>g = G \frac{m</em>1 m_2}{r^2}$
• Substituting values:
  • $F_g = 6.67 \times 10^{-11} \times \frac{70 \times 52}{1.5^2}$
• Calculation:
  • Numerator: $6.67 \times 10^{-11} \times 70 \times 52 = 2.42788 \times 10^{-7}$ (or $2.43 \times 10^{-7}$ with rounding)
  • Denominator: $1.5^2 = 2.25$
  • $F_g = \frac{2.42788 \times 10^{-7}}{2.25} = 1.079057778 \times 10^{-7} \approx 1.08 \times 10^{-7} \text{ Newtons}$

Calculator Usage

• Entering scientific notation:
  • Using the "EE" function (or similar) on the calculator.
  • Example: $6.67 \times 10^{-11}$ is entered as 6.67 EE -11.
• Order of operations:
  • Calculate the numerator first, then the denominator.
  • Divide the numerator by the denominator.
• Storing values:
  • Using the store (STO) button to save intermediate results for later use.

Common Mistakes

• Incorrectly entering scientific notation into the calculator.
• Forgetting to square the distance (r).
• Not dividing the numerator by the denominator.

Gravitational Force Between Earth and Moon

• Objective: To calculate the gravitational force between the Earth and the Moon.
• Given:
  • Moon's mass ($m_1$) = $7.34 \times 10^{22}$ kg
  • Earth's mass ($m_2$) = $6 \times 10^{24}$ kg
  • Distance between centers (r) = $3.88 \times 10^8$ meters
  • Gravitational constant ($G$) = $6.67 \times 10^{-11}$
• Formula:
  • $F<em>g = G \frac{m</em>1 m_2}{r^2}$
• Substituting values:
  • $F_g = 6.67 \times 10^{-11} \times \frac{7.34 \times 10^{22} \times 6 \times 10^{24}}{(3.88 \times 10^8)^2}$