Question

1. which of the following graphs accurately shows the force of gravity vs mass? (graphs with force (n) and mass (kg) axes, four graphs labeled a, b, c, d)
2. which of the following graphs accurately shows the force of gravity vs distance from the center? (graphs with force (n) and distance axes, four graphs labeled a, b, c, d)
3. two students are sitting 1.5 m apart. one student has a mass of 70 kg and the other has a mass of 52 kg. what is the gravitational force between them (dont forget about g!!!!)?
4. what gravitational force does the moon produce on the earth if their centers are 3.84 x 10⁸ m apart and the moon has a mass of 7.36 x 10²² kg? (hint: the mass of the earth is on your formula chart.)

Explanation:

Question 14 (Force of Gravity vs Mass Graph)

Step1: Recall the formula for gravitational force

The gravitational force (weight) on an object near the Earth's surface is given by \( F = mg \), where \( F \) is force, \( m \) is mass, and \( g \) is the acceleration due to gravity (a constant). This is a linear relationship (\( y = mx + b \) with \( b = 0 \) and slope \( g \)).

Step2: Analyze the graphs

A linear relationship between force (y - axis) and mass (x - axis) should be a straight line passing through the origin. So we look for the graph with a straight line starting from (0,0) and increasing linearly. For example, if Graph B is a straight line with a positive slope through the origin, it represents \( F = mg \) correctly.

Question 15 (Force of Gravity vs Distance from Center)

Step1: Recall the universal law of gravitation

The gravitational force between two objects is given by \( F=\frac{Gm_1m_2}{r^{2}} \), where \( r \) is the distance between their centers. For a fixed mass (e.g., an object and the Earth), \( F\propto\frac{1}{r^{2}} \). This is a non - linear relationship, and the force decreases as the square of the distance increases.

Step2: Analyze the graphs

An inverse - square relationship will be a curve that starts high when \( r \) is small and decreases rapidly as \( r \) increases. So we look for the graph with a curve that has a shape consistent with \( y=\frac{k}{x^{2}} \) (where \( y = F \) and \( x = r \)). For example, if Graph D is a curve that decreases as \( 1/r^{2} \), it represents the relationship correctly.

Question 16 (Gravitational Force between Two Students)

Step1: Recall the universal law of gravitation

The formula for the gravitational force between two objects is \( F = G\frac{m_1m_2}{r^{2}} \), where \( G=6.67\times 10^{-11}\space Nm^{2}/kg^{2} \), \( m_1 = 70\space kg \), \( m_2=52\space kg \), and \( r = 1.5\space m \).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Question 17 (Gravitational Force between Moon and Earth)

Answer:

The graph that shows a linear relationship (straight line through the origin) between force of gravity and mass (e.g., Graph B or the one with a straight line where force increases proportionally with mass).