Question

1. what is the gravitational force between two 60.0 kg people sitting 100 m apart?

a. $2.4 \times 10^{-11}$ n
b. $2.4 \times 10^{-9}$ n
c. $3.6 \times 10^{-1}$ n
d. $3.6 \times 10^{1}$ n

Explanation:

Step1: Recall Gravitational Force Formula

The formula for gravitational force between two objects is \( F = G\frac{m_1m_2}{r^2} \), where \( G = 6.67\times 10^{-11}\, \text{N}\cdot\text{m}^2/\text{kg}^2 \), \( m_1 = m_2 = 60.0\,\text{kg} \), and \( r = 100\,\text{m} \).

Step2: Substitute Values into Formula

Substitute \( m_1 = 60.0\,\text{kg} \), \( m_2 = 60.0\,\text{kg} \), \( r = 100\,\text{m} \), and \( G = 6.67\times 10^{-11}\, \text{N}\cdot\text{m}^2/\text{kg}^2 \) into the formula:

$$ F = 6.67\times 10^{-11} \times \frac{60.0\times 60.0}{100^2} $$

Step3: Calculate Numerator and Denominator

First, calculate the numerator: \( 60.0\times 60.0 = 3600 \).
Then, calculate the denominator: \( 100^2 = 10000 \).
Now, the fraction becomes \( \frac{3600}{10000} = 0.36 \).

Step4: Multiply with G

Multiply \( 6.67\times 10^{-11} \) by \( 0.36 \):

$$ F = 6.67\times 10^{-11} \times 0.36 \approx 2.4\times 10^{-11}\, \text{N} $$

Answer:

a. \( 2.4\times 10^{-11}\, \text{N} \)