Physics Flashcards: Calculate Gravitational Force Mathematically

What this deck covers

This deck focuses on Calculate Gravitational Force Mathematically, giving you a quick way to review the definitions, rules, and examples that matter most for Physics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What happens to $F$ if the distance $r$ between two masses is doubled?

Answer: $F\text{ becomes }\frac{1}{4}\text{ as large}$. Force varies as $\frac{1}{r^2}$, so $(2r)^2=4$ in denominator.

Flashcard 2: Find $m_2$ in terms of $F$ using $F=G\frac{m_1m_2}{r^2}$.

Answer: $m_2=\frac{Fr^2}{Gm_1}$. Isolate $m_2$ by multiplying both sides by $r^2/(Gm_1)$.

Flashcard 3: Calculate weight $W$ for $m=2\ \text{kg}$ in a field $g=10\ \text{m/s}^2$.

Answer: $20\ \text{N}$. Direct multiplication: $W=2\times10=20$.

Flashcard 4: State the relationship between gravitational force and field strength for a test mass $m$.

Answer: $F=mg$. Force equals mass times gravitational field strength.

Flashcard 5: What happens to $F$ if the distance $r$ between two masses is halved?

Answer: $F\text{ becomes }4\text{ times as large}$. Force varies as $\frac{1}{r^2}$, so $(\frac{r}{2})^2=\frac{1}{4}$ in denominator.

Flashcard 6: What happens to $F$ if the separation distance doubles from $r$ to $2r$?

Answer: $F\to\frac{F}{4}$. Force varies as $\frac{1}{r^2}$, so doubling $r$ gives $\frac{1}{4}$ the force.

Flashcard 7: Identify the SI unit of gravitational force $F$.

Answer: $\text{N}$. Force is measured in newtons in the SI system.

Flashcard 8: State the formula for gravitational potential energy of two masses separated by distance $r$.

Answer: $U=-G\frac{m_1m_2}{r}$. Negative sign indicates attractive force; zero at infinite separation.

Flashcard 9: What happens to $F$ if the separation distance is halved from $r$ to $\frac{r}{2}$?

Answer: $F\to^4F$. Halving distance means $r^2\to\frac{r^2}{4}$, so force quadruples.

Flashcard 10: What value of the gravitational constant should you use in SI calculations?

Answer: $G=6.67\times10^{-11}\ \text{N}\cdot\text{m}^2\cdot\text{kg}^{-2}$. Standard value used in SI unit calculations.

Flashcard 11: State the formula for the magnitude of gravitational force between two point masses.

Answer: $F=G\frac{m_1m_2}{r^2}$. Newton's law of universal gravitation relates force to masses and inverse square of distance.

Flashcard 12: Identify the meaning of $r$ in $F=G\frac{m_1m_2}{r^2}$.

Answer: $r=\text{center-to-center distance between the masses}$. Distance measured from center of mass to center of mass.

Flashcard 13: Identify the SI unit of mass $m$ used in Newton's law of gravitation.

Answer: $\text{kg}$. Mass is measured in kilograms in SI units.

Flashcard 14: Identify the variable in $F=G\frac{m_1m_2}{r^2}$ that represents center-to-center separation.

Answer: $r$. Distance between centers of the two masses.

Flashcard 15: What is the ratio $\frac{F_2}{F_1}$ if both masses double and distance stays the same?

Answer: $4$. Doubling both masses gives $2\times^2=4$ times the force.

Flashcard 16: What is the SI unit of the gravitational constant $G$?

Answer: $\text{N}\cdot\text{m}^2\cdot\text{kg}^{-2}$. Derived from $F=ma$ and dimensional analysis of the formula.

Flashcard 17: Calculate $F$ for $m_1=2\ \text{kg}$, $m_2=3\ \text{kg}$, $r=1\ \text{m}$.

Answer: $F\approx^4.00\times10^{-10}\ \text{N}$. Calculate: $F=6.67×10^{-11}×2×3/1^2=4.00×10^{-10}$ N.

Flashcard 18: What happens to $F$ if one mass doubles from $m_1$ to $2m_1$ (all else constant)?

Answer: $F\to^2F$. Force is directly proportional to each mass.

Flashcard 19: Find $r$ in terms of $F$ using $F=G\frac{m_1m_2}{r^2}$.

Answer: $r=\sqrt{G\frac{m_1m_2}{F}}$. Solve for $r$ by taking square root of rearranged equation.

Flashcard 20: Calculate $F$ for $m_1=1\ \text{kg}$, $m_2=1\ \text{kg}$, $r=2\ \text{m}$.

Answer: $F\approx^1.67\times10^{-11}\ \text{N}$. Calculate: $F=6.67×10^{-11}×1×1/2^2=1.67×10^{-11}$ N.

Flashcard 21: State the formula for gravitational field strength $g$ at distance $r$ from mass $M$.

Answer: $g=G\frac{M}{r^2}$. Field strength is force per unit mass at that location.

Flashcard 22: Identify the SI unit of distance $r$ used in $F=G\frac{m_1m_2}{r^2}$.

Answer: $\text{m}$. Distance is measured in meters in SI units.

Flashcard 23: Calculate the ratio $\frac{F_2}{F_1}$ if $r$ changes from $r_1$ to $r_2$ with masses constant.

Answer: $\frac{F_2}{F_1}=\left(\frac{r_1}{r_2}\right)^2$. Ratio of forces equals inverse ratio of distances squared.

Flashcard 24: What is the direction of the gravitational force on each mass in a two-body system?

Answer: $\text{Along the line joining the centers, toward the other mass}$. Gravity is always attractive between masses.

Flashcard 25: What is the ratio $\frac{F_2}{F_1}$ if distance changes from $r$ to $3r$ (masses unchanged)?

Answer: $\frac{1}{9}$. Since $F\propto\frac{1}{r^2}$, tripling $r$ gives $\frac{1}{9}$ the force.

Flashcard 26: What is the value of the universal gravitational constant $G$ in SI units?

Answer: $G=6.67\times10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$. Fundamental constant determined experimentally by Cavendish.

Flashcard 27: What happens to $F$ if one mass (for example $m_1$) is doubled while $r$ is constant?

Answer: $F\text{ doubles}$. Force is directly proportional to each mass.

Flashcard 28: Calculate $g$ at $r=2R$ from a planet: if $g(R)=g_0$, what is $g(2R)$?

Answer: $g(2R)=\frac{g_0}{4}$. Field follows inverse square law: $g∝1/r^2$, so doubling $r$ gives $g/4$.

Flashcard 29: Calculate $F$ on a $3\ \text{kg}$ mass where the gravitational field strength is $g=10\ \text{m}\cdot\text{s}^{-2}$.

Answer: $F=30\ \text{N}$. $F=mg=3\times10=30$ N using weight formula.

Flashcard 30: Which option gives the correct proportionality for Newtonian gravity with distance: $F\propto r$, $F\propto \frac{1}{r}$, or $F\propto \frac{1}{r^2}$?

Answer: $F\propto \frac{1}{r^2}$. Inverse square law: force decreases with square of distance.

Flashcard 31: Identify the sign of gravitational potential energy $U$ for two isolated masses at finite $r$.

Answer: $U<0$. Attractive force means bound system has negative energy.

Flashcard 32: State the formula for gravitational field strength due to a mass $M$ at distance $r$.

Answer: $g=G\frac{M}{r^2}$. Field strength is force per unit mass at distance $r$.

Flashcard 33: State the relationship between weight $W$ and gravitational field strength $g$ for mass $m$.

Answer: $W=mg$. Weight equals mass times gravitational field strength.