Compare Gravitational and Electric Forces - Physics

1. If $m_1$ doubles (all else constant), by what factor does $F_g$ change?

   $F_g$ doubles. Force is directly proportional to each mass in the numerator.

2. If both charges change sign ($q_1\to -q_1$, $q_2\to -q_2$), what happens to the electric force direction?

   Direction is unchanged (still attractive or still repulsive). Product $q_1q_2$ stays same sign when both flip.

3. What is the formula for the magnitude of the gravitational force between two point masses?

   $F_g=G\frac{m_1m_2}{r^2}$. Newton's law of universal gravitation with inverse square dependence on distance.

4. What is the direction rule for the electric force on $q_1$ due to $q_2$?

   Along the line joining them; toward unlike, away from like. Electric forces act along the line between charges with direction based on sign.

5. What is the quantitative ratio $\frac{F_e}{F_g}$ for two particles separated by the same $r$?

   $\frac{F_e}{F_g}=\frac{k|q_1q_2|}{Gm_1m_2}$. Divide Coulomb's law by Newton's law to compare force magnitudes directly.

6. If only one charge changes sign ($q_1\to -q_1$), what happens to the electric force direction?

   Direction reverses (attractive becomes repulsive or vice versa). Product $q_1q_2$ changes sign when only one flips.

7. What is the correct sign behavior: can gravitational forces be repulsive, attractive, or both?

   Gravitational force is always attractive. Masses always attract; no negative mass exists.

8. Identify the distance dependence shared by $F_g$ and $F_e$ for point particles.

   Both follow an inverse-square law: $F\propto \frac{1}{r^2}$. Force decreases with square of distance for both interactions.

9. If the separation doubles, by what factor does each of $F_g$ and $F_e$ change?

   Each becomes $\frac{1}{4}$ of its original value. Both forces have $\frac{1}{r^2}$ dependence, so doubling $r$ gives $\frac{1}{2^2}=\frac{1}{4}$.

10. If separation doubles, by what factor do both $F_g$ and $F_e$ change for point particles?

    They become $\frac{1}{4}$ as large. Inverse-square law: doubling $r$ gives $F\propto\frac{1}{(2r)^2}=\frac{1}{4r^2}$.

11. If $q_1$ changes from $+q$ to $-q$ (same magnitude), what happens to $|F_e|$?

    $|F_e|$ is unchanged. Magnitude depends on $|q_1q_2|$, which is same for $+q$ or $-q$.

12. Identify the units of Coulomb's constant $k$ in $F_e=k\frac{|q_1q_2|}{r^2}$.

    $\mathrm{N\,m^2/C^2}$. Similar to $G$ but with charge (coulombs) instead of mass (kg).

13. For an electron and a proton, what is the ratio $\frac{F_e}{F_g}$ (order of magnitude)?

    $\frac{F_e}{F_g}\approx10^{39}$. Even larger ratio for electron-proton due to electron's tiny mass.

14. What is the correct sign behavior: can electric forces be attractive, repulsive, or both?

    Electric force can be attractive or repulsive. Like charges repel, opposite charges attract.

15. Which force can be attractive or repulsive depending on the interacting objects: gravity or electric?

    Electric can attract or repel; gravity is always attractive. Opposite charges attract, like charges repel; masses always attract.

16. For fixed $m_1,m_2,q_1,q_2$, does changing $r$ change the ratio $\frac{F_e}{F_g}$?

    No; $\frac{F_e}{F_g}$ is independent of $r$. Both forces have same $r^2$ dependence, which cancels in ratio.

17. If separation triples, by what factor do both $F_g$ and $F_e$ change for point particles?

    They become $\frac{1}{9}$ as large. Inverse-square law: tripling $r$ gives $F\propto\frac{1}{(3r)^2}=\frac{1}{9r^2}$.

18. If the separation triples, by what factor does each of $F_g$ and $F_e$ change?

    Each becomes $\frac{1}{9}$ of its original value. Tripling distance gives $\frac{1}{3^2}=\frac{1}{9}$ due to inverse square law.

19. What is the formula for the electric force magnitude between two point charges (Coulomb's law)?

    $F_e = k\frac{|q_1 q_2|}{r^2}$. Coulomb's law gives force between point charges.

20. Which option gives the correct SI units: $k$ in $\text{N}\cdot\text{m}^2/\text{C}^2$ or $\text{N}\cdot\text{m}^2/\text{kg}^2$?

    $k:\ \text{N}\cdot\text{m}^2/\text{C}^2$. Coulomb's constant has units of force×area per charge squared.

21. Which option best compares force strengths for elementary particles: $F_e$ or $F_g$?

    $F_e\gg F_g$ (by about $10^{36}$ to $10^{39}$). Electric forces dominate by many orders of magnitude at particle scale.

22. Which option gives the correct SI units: $G$ in $\text{N}\cdot\text{m}^2/\text{kg}^2$ or $\text{N}\cdot\text{m}^2/\text{C}^2$?

    $G:\ \text{N}\cdot\text{m}^2/\text{kg}^2$. Gravitational constant has units of force×area per mass squared.

23. Find the ratio $\frac{F_e}{F_g}$ for two identical particles with charge $q$ and mass $m$.

    $\frac{F_e}{F_g}=\frac{k q^2}{G m^2}$. Simplifies since $q_1=q_2=q$ and $m_1=m_2=m$.

24. What is the formula for the magnitude of the electric (Coulomb) force between two point charges?

    $F_e=k\frac{|q_1q_2|}{r^2}$. Coulomb's law shows electric force also follows inverse square law like gravity.

25. If $m_1,m_2,q_1,q_2$ are all doubled (same $r$), by what factor does $\frac{F_e}{F_g}$ change?

    No change; $\frac{F_e}{F_g}$ stays the same. Ratio cancels the factor of 2 in both numerator and denominator.

26. If $m_1$ is doubled (others fixed), by what factor does $F_g$ change?

    $F_g$ doubles. Force is directly proportional to each mass.

27. If $q_1$ is doubled (others fixed), by what factor does $F_e$ change?

    $F_e$ doubles. Force is directly proportional to each charge magnitude.

28. For two protons, what is the ratio $\frac{F_e}{F_g}$ (order of magnitude)?

    $\frac{F_e}{F_g}\approx10^{36}$. Electric force dominates at atomic scale due to large charge-to-mass ratio.

29. If both charges reverse sign ($q_1\to -q_1$ and $q_2\to -q_2$), what happens to the force type?

    It stays the same (attractive stays attractive, repulsive stays repulsive). Product $q_1q_2$ has same sign when both charges flip, preserving force type.

30. What is the ratio $\frac{F_e}{F_g}$ for the same separation $r$ between particles?

    $\frac{F_e}{F_g}=\frac{k|q_1 q_2|}{G m_1 m_2}$. Ratio cancels $r^2$ terms, leaving charge and mass factors.

31. Identify the units of the gravitational constant $G$ in $F_g=G\frac{m_1m_2}{r^2}$.

    $\mathrm{N\,m^2/kg^2}$. Derived from $F=G\frac{m^2}{r^2}$ where $F$ has units of newtons.

32. Which interaction is stronger between two electrons: electric or gravitational (quantitatively)?

    Electric; $\frac{F_e}{F_g}\approx 10^{42}$ for two electrons. Electric force vastly exceeds gravity for elementary particles.

33. Find $\frac{F_e}{F_g}$ when $q_1=q_2=q$ and $m_1=m_2=m$ (same $r$).

    $\frac{F_e}{F_g}=\frac{kq^2}{Gm^2}$. Simplifies when charges and masses are equal, showing dependence on $\frac{q}{m}$ ratio.

34. Which interaction is stronger between two protons: electric or gravitational (quantitatively)?

    Electric; $\frac{F_e}{F_g}\approx 10^{36}$ for two protons. Electromagnetic force dominates at atomic scales.

35. What is the formula for the gravitational force magnitude between two point masses?

    $F_g = G\frac{m_1 m_2}{r^2}$. Newton's law of universal gravitation for point masses.

36. Identify the correct constants: $G\approx 6.67\times 10^{-11}$ and $k\approx 8.99\times 10^9$ (SI).

    $G\approx 6.67\times 10^{-11}$, $k\approx 8.99\times 10^9$. Values show $k\gg G$ in SI units.

37. What is the direction rule for the gravitational force on $m_1$ due to $m_2$?

    Along the line joining them, toward $m_2$. Gravity is always attractive, pulling masses together along their connecting line.

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