Gravitational Force - AP Physics 1

1. What does $r$ stand for in the gravitational force formula?

   Distance between the centers of masses. Distance measured from center to center, not surface to surface.

2. What happens to gravitational force if $m_1$ is tripled?

   Force triples. Force is directly proportional to each mass individually.

3. What principle does Newton's law of universal gravitation illustrate?

   Every mass attracts every other mass. Newton's law applies universally to all objects with mass.

4. Describe the effect of mass on gravitational attraction.

   Greater mass, stronger attraction. More massive objects exert stronger gravitational pulls.

5. What does $m_2$ stand for in the gravitational force formula?

   Mass of the second object. Second object's mass in the gravitational force equation.

6. How does the gravitational force change with altitude?

   Decreases with altitude. Higher altitude means greater distance from Earth's center.

7. State the formula for gravitational force between two masses.

   $F = G \frac{m_1 m_2}{r^2}$. Newton's universal gravitation formula relating force to masses and distance squared.

8. What is the relationship between gravitational force and gravitational field strength?

   Force = mass × field strength. Gravitational field strength equals force per unit mass.

9. What is required for gravitational force to exist between two objects?

   Both objects have mass. Only objects with mass can exert or experience gravitational force.

10. How does gravitational force compare on different planets?

    Varies with planetary mass and radius. Different planetary properties create different gravitational field strengths.

11. What is the gravitational force exerted by Earth on a 1 kg object at its surface?

    Approximately $9.8 \text{ N}$. Weight of 1 kg object equals mass times Earth's surface gravity.

12. What is the gravitational force between two 1 kg masses 1 m apart?

    $6.674 \times 10^{-11} \text{ N}$. Substituting $m_1 = m_2 = 1$ kg, $r = 1$ m into Newton's formula.

13. State the relationship between gravitational force and distance.

    Inversely proportional to $r^2$. Force decreases rapidly as distance increases due to square relationship.

14. What is the effect on gravitational force if the distance $r$ is doubled?

    Force is quartered. Force varies as $1/r^2$, so doubling distance reduces force by factor of 4.

15. What happens to gravitational force if one mass doubles?

    Force doubles. Force is directly proportional to each mass in the equation.

16. What is the gravitational force on a satellite orbiting Earth?

    Centripetal force maintaining orbit. Gravitational attraction provides the inward force needed for circular motion.

17. Find gravitational force if $m_1 = 2 \text{ kg}$, $m_2 = 3 \text{ kg}$, $r = 1 \text{ m}$.

    $4.00 \times 10^{-10} \text{ N}$. Using the gravitational force formula with the specified masses and distance.

18. How does gravitational force change if both masses double?

    Force quadruples. Each mass doubles independently, so total force increases by $2 \times 2 = 4$.

19. Identify the units of the gravitational constant $G$.

    N m²/kg². Derived from force units divided by mass squared times distance squared.

20. What is the value of the gravitational constant $G$?

    $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$. Standard value of the universal gravitational constant.

21. Identify the type of force gravitational force is considered.

    Attractive force. Gravity always pulls objects together, never pushes them apart.

22. What does $G$ represent in the gravitational force formula?

    Gravitational constant. Universal constant that makes the gravitational formula dimensionally consistent.

23. What is the relationship between gravitational force and gravitational potential energy?

    Potential energy depends on force and distance. Potential energy is the integral of force over distance.

24. What happens to gravitational force if both $m_1$ and $m_2$ double?

    Force quadruples. Each mass doubles, creating a $2 \times 2 = 4$ factor increase.

25. State the relationship between gravitational force and mass.

    Directly proportional. Larger masses produce stronger gravitational forces.

26. What role does gravitational force play in planetary orbits?

    Keeps planets in orbit. Solar gravity provides centripetal force maintaining planetary orbital motion.

27. In which direction does gravitational force act?

    Towards the center of the masses. Gravity always pulls objects toward each other's centers.

28. How does gravitational force change when $r$ is halved?

    Force quadruples. Halving distance means $r^2$ becomes $r^2/4$, so force increases 4 times.

29. How does gravitational force affect tides on Earth?

    Causes tidal forces. Moon's gravity creates differential forces causing ocean tides.

30. How does gravitational force influence satellite motion?

    Provides necessary centripetal force. Earth's gravity supplies the centripetal acceleration for orbital motion.

31. What does $m_1$ stand for in the gravitational force formula?

    Mass of the first object. First object's mass in the gravitational force equation.

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