Evidence for Gravity - Middle School Physical Science

1. What happens to gravitational force if both masses are doubled while $r$ stays constant?

   Force becomes $4$ times as large. Doubling both masses multiplies force by $2 \times 2 = 4$.

2. Identify the independent variable when a simulation changes only distance to test its effect on $F_g$.

   Distance $r$. Independent variable is what you change; dependent is what you measure.

3. What happens to gravitational force if one mass is doubled while $r$ stays constant?

   Force doubles. Force is directly proportional to each mass, so doubling one mass doubles force.

4. Which change best supports the claim that gravity increases with mass in a simulation?

   Increase $m_1$ or $m_2$ while keeping $r$ constant. Since $F \propto m_1m_2$, increasing either mass while fixing distance shows force increases.

5. Identify the best conclusion if a simulation shows $F$ stays the same when both masses swap positions.

   Gravitational force depends on masses and distance, not on which mass is labeled $1$ or $2$. The formula is symmetric in $m_1$ and $m_2$, so swapping them doesn't change $F$.

6. Which option states Newton's third law for gravitational interaction between two masses?

   Forces are equal in magnitude and opposite in direction. Action-reaction pairs have equal magnitude but opposite directions.

7. Identify the best claim supported if a simulation shows force decreases rapidly as $r$ increases.

   Gravitational force decreases with distance by an inverse-square pattern. Rapid decrease with distance indicates inverse-square relationship.

8. Which statement is supported if a simulation shows equal and opposite forces on two interacting masses?

   Gravitational forces come in equal-magnitude, opposite-direction pairs. Newton's third law: every gravitational force has an equal and opposite reaction force.

9. Find the missing evidence: If a graph of $F_g$ vs. $r$ is consistent with $\frac{1}{r^2}$, what claim is supported?

   Gravitational force follows an inverse-square law with distance. Graph matching $\frac{1}{r^2}$ pattern confirms the inverse-square law.

10. Which evidence from a simulation best supports that gravity is always attractive?

    Objects always accelerate toward each other, never away. Attractive force means objects move toward each other, never repel.

11. If a simulation doubles $m_1$ while $m_2$ and $r$ stay constant, what happens to $F$?

    It doubles. Force is directly proportional to each mass, so doubling one mass doubles the force.

12. Which graph shape best matches the model prediction for $F$ versus $m_1$ when $m_2$ and $r$ are constant?

    A straight line through the origin (directly proportional). Direct proportionality between $F$ and $m_1$ creates a linear relationship through origin.

13. Which graph shape best matches the model prediction for $F$ versus $r$ when masses are constant?

    A decreasing curve proportional to $\frac{1}{r^2}$. The inverse square relationship creates a hyperbolic curve that decreases rapidly.

14. In a simulation, which variable must be controlled to isolate the effect of distance on $F$?

    Keep $m_1$ and $m_2$ constant. Controlling masses isolates distance effects since $F$ depends on both variables.

15. A model shows Earth pulls on the Moon with force $F$. What force does the Moon exert on Earth?

    Also $F$, in the opposite direction. Newton's third law: forces between objects are equal and opposite.

16. What is the formula for gravitational force between two masses?

    $F_g = G\frac{m_1m_2}{r^2}$. Newton's law shows force depends on both masses and inversely on distance squared.

17. If a model doubles the distance $r$, what happens to the force $F$ according to $F\propto\frac{1}{r^2}$?

    It becomes $\frac{1}{4}$ of the original force. Force varies as $\frac{1}{r^2}$, so doubling $r$ gives $\frac{1}{(2r)^2} = \frac{1}{4}$ of original.

18. Which change best supports the claim that gravity decreases with distance in a simulation?

    Increase $r$ while keeping $m_1$ and $m_2$ constant. Since $F \propto \frac{1}{r^2}$, increasing distance while fixing masses shows force decreases.

19. Which model outcome best supports that gravitational interactions act at a distance without contact?

    Forces occur even when objects are not touching. Gravity acts through empty space without requiring physical contact between objects.

20. What happens to gravitational field strength $g$ if distance from the planet center is doubled?

    $g$ becomes $\frac{1}{4}$ as large. Field strength follows same inverse-square law as gravitational force.

21. Which relationship should a correct gravity model show between force and distance?

    Inverse-square: $F_g \propto \frac{1}{r^2}$. Force decreases with the square of distance, not linearly.

22. Which model result supports the claim that gravity is always attractive, not repulsive?

    Objects accelerate toward each other, not away, for all tested masses. Attractive force means objects always pull together, never push apart.

23. What is the formula for gravitational field strength due to a mass $M$ at distance $r$?

    $g = G\frac{M}{r^2}$. Field strength at a point depends on source mass and distance from it.

24. What is the direction of the gravitational force on each mass in a two-body model?

    Along the line joining centers, toward the other mass. Gravity always pulls objects directly toward each other.

25. If a model triples the distance $r$, what happens to the force $F$ according to $F\propto\frac{1}{r^2}$?

    It becomes $\frac{1}{9}$ of the original force. Force varies as $\frac{1}{r^2}$, so tripling $r$ gives $\frac{1}{(3r)^2} = \frac{1}{9}$ of original.

26. What happens to gravitational force if distance $r$ is doubled in a simulation?

    Force becomes $\frac{1}{4}$ as large. Doubling distance makes $r^2$ become $4r^2$, reducing force by factor of 4.

27. Which relationship should a correct gravity model show between force and each mass?

    Direct: $F_g \propto m_1$ and $F_g \propto m_2$. Force increases linearly with each mass independently.

28. Which variable in $F_g = G\frac{m_1m_2}{r^2}$ represents the distance between centers?

    $r$. Distance is measured between the centers of mass of the two objects.

29. If a model uses $g = 10\ \text{N/kg}$ and $m = 3\ \text{kg}$, what is $F_g$?

    $30\ \text{N}$. Using $F_g = mg$: $F_g = 3\ \text{kg} \times 10\ \text{N/kg} = 30\ \text{N}$.

30. What does the variable $r$ represent in the model $F = G\frac{m_1 m_2}{r^2}$?

    Center-to-center distance between the two masses. The distance $r$ is measured from one object's center to the other's center.

31. In a simulation, which variable must be controlled to isolate the effect of mass on $F$?

    Keep $r$ constant. Controlling distance isolates mass effects since $F$ depends on both variables.

32. If a simulation doubles both $m_1$ and $m_2$ while $r$ stays constant, what happens to $F$?

    It becomes $4$ times larger. Doubling both masses multiplies force by $2 \times 2 = 4$ since $F \propto m_1m_2$.

33. Identify the best claim supported if a simulation shows higher force for larger $m_1$ at fixed $r$.

    Gravitational force increases as mass increases. Direct proportionality means larger mass produces larger force.

34. What happens to gravitational force if distance $r$ is tripled in a simulation?

    Force becomes $\frac{1}{9}$ as large. Tripling distance makes $r^2$ become $9r^2$, reducing force by factor of 9.

35. Which evidence from an orbit simulation best supports that gravity provides centripetal force?

    The orbiting object continuously accelerates toward the central mass. Gravity pulls the orbiting object inward, providing the centripetal acceleration for circular motion.

36. What is the formula for gravitational force between two masses in a model?

    $F = G\frac{m_1 m_2}{r^2}$. Newton's law shows force depends on both masses and inverse square of distance.

37. What does a downward arrow labeled $F_g$ on a free-body diagram represent?

    The gravitational force (weight) acting toward the attracting body. Weight is the gravitational force pulling an object toward the planet or star.

38. What is the relationship between weight and mass near a planet in a model?

    $F_g = mg$. Near a planet's surface, weight equals mass times gravitational field strength.

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