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Topic 2.6: Practice Sheet — Gravitational Force

Name: _______________________________ Date: _______________ Period: ______

Directions: For ratio problems, write the full symbolic equation with the changed variables substituted in FIRST, then simplify. For numeric problems, solve symbolically before substituting.

Warm-Up Level (straightforward, one-step)

  1. Write Newton's law of universal gravitation. What does each symbol represent?
  2. Two objects are a fixed distance apart. If both of their masses are doubled, what happens to the gravitational force between them?

Standard Level (multi-step, matches typical AP Classroom depth)

  1. Two objects are a distance $r$ apart, with gravitational force $F_g$ between them. If the distance is cut in half, find the new force in terms of $F_g$.
  2. A planet has 4 times Earth's mass and twice Earth's radius. An object weighs $W_E$ on Earth. Find the object's weight on this planet, in terms of $W_E$.
  3. A 50 kg person stands on a scale in an elevator accelerating downward at 1.5 m/s². Using $g=9.8\text{ m/s}^2$, find the scale's reading.

AP-Level (multi-part: calculate + justify/represent/predict-a-change)

  1. A satellite orbits Earth at distance $r$ from Earth's center, where the gravitational force provides the centripetal force needed to keep it in orbit. a) Write a symbolic expression for the gravitational field $g$ at the satellite's location, in terms of $G$, Earth's mass $M_E$, and $r$. b) If the satellite moves to an orbit at distance $2r$, explain — without recalculating from scratch — whether the gravitational field there is more than, less than, or exactly one-fourth its original value.
  2. A person's true weight on Earth is $mg$. Explain, using forces (not just the word "gravity"), why an astronaut orbiting Earth in the space station experiences apparent weightlessness even though Earth's gravitational field at that altitude is still nearly as strong as it is at the surface.

Progress Check Style (evaluate the method — AP Classroom format)

  1. A person stands on a scale in an elevator that is moving downward while slowing down. Which of the following correctly describes the relationship between the scale's reading (apparent weight) and the person's true weight $mg$? (A) The scale reads less than $mg$, because the elevator's acceleration is directed upward (B) The scale reads less than $mg$, because the elevator's acceleration is directed downward (C) The scale reads more than $mg$, because the elevator's acceleration is directed upward (D) The scale reads exactly $mg$, because the elevator is still moving downward

Progress-Check-Aligned Practice (extra depth — same style as your unit test)

  1. Two planets orbit a distant star of mass $M$. Planet A has mass $2m$ and orbits at distance $2R$ from the star's center. Planet B has mass $m$ and orbits at distance $R$ from the star's center. Ignoring the planets' gravitational effect on each other, write a symbolic expression for the magnitude of the net gravitational force exerted on Planet B by the star.
  2. A hypothetical planet has twice Earth's radius and twice Earth's mass. An object weighs $W_E$ on Earth's surface. Derive a symbolic expression for the object's weight on the hypothetical planet, written as a single coefficient times $W_E$, and show the full derivation rather than just the final ratio.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.