Gravitational Force - AP Physics C Mechanics

1. What is the direction of gravitational force between two masses?

   Along the line joining the two masses. Force vector points along the line connecting mass centers.

2. What is the relationship between $g$ and $G$ on Earth's surface?

   $g = G \frac{M}{R^2}$, where $M$ is Earth's mass, $R$ is radius. Relates surface gravity to Earth's mass and radius.

3. Describe the inverse-square law in gravitation.

   Force inversely proportional to square of distance. Fundamental relationship describing how gravity weakens with distance.

4. Define gravitational field strength, $g$.

   $g = \frac{F}{m}$, where $F$ is force and $m$ is mass. Force per unit mass at a point in the field.

5. What is the effect of gravity on a pendulum?

   Provides restoring force for motion. Gravity creates torque that drives pendulum oscillations.

6. What type of force is gravitational force?

   It is an attractive force. Gravity always pulls masses toward each other.

7. Calculate $F$ if $m_1 = 5 \text{ kg}$, $m_2 = 10 \text{ kg}$, $r = 3 \text{ m}$.

   $3.7044 \times 10^{-10} \text{ N}$. Using $F = G\frac{m_1 m_2}{r^2} = G\frac{(5)(10)}{9}$.

8. What is the universal gravitational constant, $G$?

   $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$. Fundamental constant in Newton's gravitational law.

9. Identify the relationship between weight and gravitational force.

   Weight is gravitational force on a mass. Weight equals mass times gravitational field strength.

10. Calculate the gravitational force between two $1 \text{ kg}$ masses $1 \text{ m}$ apart.

    $6.674 \times 10^{-11} \text{ N}$. Using $F = G\frac{m_1 m_2}{r^2}$ with given values.

11. What is a microgravity environment?

    Very low effective gravitational force. Nearly weightless conditions found in space stations.

12. Is gravitational force a vector or scalar quantity?

    Vector. Has both magnitude and direction toward mass center.

13. What is the formula for gravitational potential energy?

    $U = -G \frac{m_1 m_2}{r}$. Negative energy due to attractive nature of gravity.

14. How does gravitational force change if $r$ is halved?

    Force increases by a factor of 4. Force varies as $\frac{1}{r^2}$, so halving $r$ gives $4$ times force.

15. What determines the strength of a gravitational field at a point?

    Mass and distance from the mass. Field strength follows inverse square law with distance.

16. What role does gravity play in planetary orbits?

    Gravity provides the centripetal force. Gravitational attraction maintains stable orbital paths.

17. Differentiate gravitational force and gravitational field.

    Force acts on masses; field is a region. Force is interaction; field describes space around mass.

18. What is the unit of gravitational field strength?

    N/kg or m/s$^2$. Equivalent units for gravitational acceleration.

19. How do mass and distance affect gravitational force?

    Force directly with mass, inversely with distance squared. Summarizes the two key variables in gravitational force.

20. What happens to gravitational force if distance doubles?

    Force is reduced to $\frac{1}{4}$ of original. Force varies as $\frac{1}{r^2}$, so doubling $r$ gives $\frac{1}{4}$ force.

21. Calculate gravitational force if $m_1 = 2 \text{ kg}$, $m_2 = 3 \text{ kg}$, $r = 2 \text{ m}$.

    $1.0026 \times 10^{-10} \text{ N}$. Using $F = G\frac{m_1 m_2}{r^2} = G\frac{(2)(3)}{4}$.

22. State Newton's law of universal gravitation equation.

    $F = G \frac{m_1 m_2}{r^2}$. Universal formula relating force to masses and distance squared.

23. Identify the SI unit of gravitational force.

    Newton (N). Standard unit for all forces in the SI system.

24. What is a gravitational field?

    A region of space with a force on masses. Space around mass where gravitational forces are experienced.

25. What is gravitational interaction?

    Mutual attraction between masses. Each mass experiences equal and opposite gravitational force.

26. What happens to gravitational force if both masses double?

    Force quadruples. Force is proportional to both masses, so $2 \times 2 = 4$.

27. If mass $m_1$ is halved, how does $F$ change?

    Force is halved. Force is directly proportional to each mass.

28. Does gravitational force act in a vacuum?

    Yes, it acts in a vacuum. Gravitational force requires no medium to propagate.

29. What is the gravitational force on a satellite in orbit?

    Provides centripetal force for orbit. Gravity supplies inward force needed for circular motion.

30. What causes gravitational attraction between two bodies?

    Mass of the bodies. Mass creates gravitational field that attracts other masses.

31. Calculate gravitational potential energy for two masses $1 \text{ kg}$ each, $1 \text{ m}$ apart.

    $-6.674 \times 10^{-11} \text{ J}$. Using $U = -G \frac{m_1 m_2}{r}$ with given masses and distance.

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