Question

f = g\frac{m_1m_2}{r^2}
f = force
g = gravitational constant
m_1 = mass of object 1
m_2 = mass of object 2
r = distance between centers of the masses

1. two students are sitting 1.50 m apart. one student has a mass of 70.0 kg and the other has a mass of 52.0 kg. what is the gravitational force between them?

example:

Explanation:

Step1: Identify known values

We know the gravitational constant \( G = 6.674\times10^{-11}\, \text{N}\cdot\text{m}^2/\text{kg}^2 \), \( m_1 = 70.0\, \text{kg} \), \( m_2 = 52.0\, \text{kg} \), and \( r = 1.50\, \text{m} \).

Step2: Substitute into the formula

Use the formula \( F = G\frac{m_1m_2}{r^2} \). Substitute the values: \( F=(6.674\times 10^{-11})\times\frac{70.0\times52.0}{(1.50)^2} \).

Step3: Calculate the numerator and denominator

First, calculate the numerator: \( 70.0\times52.0 = 3640 \). Then the denominator: \( (1.50)^2=2.25 \).

Step4: Perform the division and multiplication

Now, \( \frac{3640}{2.25}\approx1617.78 \). Then multiply by \( G \): \( F = 6.674\times 10^{-11}\times1617.78\approx 1.079\times 10^{-7}\, \text{N} \).

Answer:

The gravitational force between them is approximately \( 1.08\times 10^{-7}\, \text{N} \) (or more precisely \( 1.08\times10^{-7}\, \text{N} \) after rounding appropriately).