Question

1. at what point is the comet going to experience the greatest gravitational force and tangential velocity? why?
2. which of the following graphs accurately shows the force of gravity vs mass?
3. which of the following graphs accurately shows the force of gravity vs distance from the center?
4. 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!!!!!)?
5. 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 16 Solution:

Step1: Recall the gravitational force formula

The formula for gravitational force between two objects is $F = G\frac{m_1m_2}{r^2}$, where $G = 6.674\times 10^{-11}\ \text{N·m}^2/\text{kg}^2$, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers.

Step2: Identify the given values

Here, $m_1 = 70\ \text{kg}$, $m_2 = 52\ \text{kg}$, and $r = 1.5\ \text{m}$.

Step3: Substitute the values into the formula

First, calculate the product of the masses: $m_1m_2 = 70\times52 = 3640\ \text{kg}^2$.
Then, calculate $r^2 = (1.5)^2 = 2.25\ \text{m}^2$.
Now, substitute into the formula:
$F = 6.674\times 10^{-11}\times\frac{3640}{2.25}$
First, compute $\frac{3640}{2.25}\approx 1617.78$.
Then, multiply by $G$: $F = 6.674\times 10^{-11}\times1617.78\approx 1.03\times 10^{-7}\ \text{N}$.

Question 14 Explanation (Graph Identification):

The gravitational force $F$ on an object near the Earth's surface is given by $F = mg$, where $g$ is the acceleration due to gravity (a constant). This is a linear relationship ($F\propto m$), so the graph of force vs mass should be a straight line with a positive slope (as mass increases, force increases) and passing through the origin (when mass is 0, force is 0). Graph A shows this linear, directly proportional relationship, while B shows a negative slope, and C and D show non - linear relationships, which do not match $F = mg$.

Question 15 Explanation (Graph Identification):

The gravitational force formula is $F = G\frac{Mm}{r^2}$, which shows that the force is inversely proportional to the square of the distance ($F\propto\frac{1}{r^2}$). This is a non - linear relationship (inverse - square law). Graphs A (positive linear) and B (negative linear) show linear relationships, which are incorrect. Graph C shows a curve that does not match the inverse - square behavior, while Graph D shows a curve where force decreases rapidly as distance increases, consistent with $F\propto\frac{1}{r^2}$.

Question 13 Explanation:

Answer:

$\boldsymbol{1.03\times 10^{-7}\ \text{N}}$ (approximate value, depending on $G = 6.674\times 10^{-11}\ \text{N·m}^2/\text{kg}^2$)