Worksheet: Free Fall and Weightlessness

In this worksheet, we will practice describing the motion of objects acted on only by a constant gravitational force, moving only parallel to the force.

Q1:

Two objects, object I and object II, are both 75 m above the surface of the Moon, where the only force that acts on either of them is the gravitational force of the Moon. Neither object has any motion other than that due to its gravitational acceleration. Object I has a mass of 2.5 kg and object II has a mass of 6.5 kg.

What is the ratio of the mass of object I to the mass of object II?

What is the ratio of the gravitational force on object I to the gravitational force on object II?

What is the ratio of the acceleration toward the lunar surface of object I to the acceleration toward the lunar surface of object II?

Q2:

Two objects, object I and object II, are both 90 m above the surface of the Moon, where the only force that acts on either of them is the gravitational force of the Moon. Neither object has any motion other than that due to its gravitational acceleration. Object I and object II each have masses of 1.2 kg, and they both accelerate toward the lunar surface at 1.6 m/s2. Both objects are then elevated to a point 90 m above the lunar surface again and attached to each other to form a single compound object, and they are then released. What is the acceleration of the compound object toward the lunar surface when it is released?

Q3:

Two objects, object I and object II, are both 120 m above the surface of the Moon, where the only force that acts on either of them is the gravitational force of the Moon. Neither object has any motion other than that due to its gravitational acceleration. Object I and object II each have masses of 1.5 kg.

What is the ratio of the mass of object I to the mass of object II?

What is the ratio of the gravitational force on object I to the gravitational force on object II?

What is the ratio of the acceleration toward the lunar surface of object I to the acceleration toward the lunar surface of object II?

Q4:

An object is 36 m above the surface of the Moon; the only force that acts on the object is the gravitational force of the Moon. The object has no motion other than that due to its gravitational acceleration. The object has a mass of 2.8 kg. The object accelerates toward the lunar surface at 1.6 m/s2. The object is then split into two pieces, piece I and piece II, where piece I has a mass of 1.7 kg and piece II has a mass of 1.1 kg. The pieces are then elevated to a point 36 m above the lunar surface again and then released. What is the ratio of the acceleration toward the lunar surface of piece I to the acceleration toward the lunar surface of piece II?

Q5:

The objects I, II, and III shown in the diagram are at a height of 125 m above the surface of the Moon. The objects all have the same density and are all dropped at an instant 𝑡.

Which of the following is the relation between the masses 𝑚I, 𝑚II, and 𝑚III?

  • A𝑚<𝑚<𝑚IIIIII
  • B𝑚=𝑚=𝑚IIIIII
  • C𝑚>𝑚>𝑚IIIIII

Which of the following is the relation between the instants 𝑡I, 𝑡II, and 𝑡III at which the objects land on the surface of the Moon?

  • A𝑡=𝑡=𝑡IIIIII
  • B𝑡<𝑡<𝑡IIIIII
  • C𝑡>𝑡>𝑡IIIIII

Q6:

A bullet is fired vertically upward from the surface of Earth. What is the acceleration of the bullet toward Earth at a point halfway to the point at which the bullet changes direction and starts to fall back toward Earth?

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