# Worksheet: The Relationship between Mass and Weight

In this worksheet, we will practice applying Newton's second law of motion to define gravitational field strength as the force acting on an object per kilogram of its mass.

**Q4: **

An astronaut on Earth, where the gravitational field strength is 9.8 N/kg, has a mass of 65 kg and a weight of 637 N. The astronaut is sent to a space station, where the gravitational field strength is 9.5 N/kg.

What is the astronaut’s mass on the space station?

What is the astronaut’s weight on the space station?

**Q6: **

An astronaut who has a mass of 80 kg goes to Mars. On Mars, the astronaut applies a force of 296 N to the ground beneath her due to her weight. What is the acceleration due to gravity at the surface of Mars?

**Q7: **

The gravitational field strength of a planet becomes weaker as the distance from the planet’s surface increases. Several thousand kilometers above a planet, its gravitational field strength is 2.4 N/kg. What force, in kilonewtons, toward the planet’s surface is experienced by a spacecraft with a mass of 25,000 kg?

**Q8: **

A balloon that is initially empty is inflated by filling it with helium, as shown in the diagram. Before and after the balloon is inflated, the diagram shows a black dashed line that represents the boundary of the balloon and its contents.

Which of the following statements correctly describes how the mass of the matter within the dashed line changes before and after the balloon is inflated?

- AThe mass of the matter decreases.
- BThe mass of the matter increases.
- CThe mass increases at first and then goes back to its initial state at equilibrium.
- DThe mass of the matter does not change.
- EThe mass of the matter does not change since gases are not considered matter.

Which of the following statements correctly describes how the weight of the matter within the dashed line changes before and after the balloon is inflated?

- AThe weight of the matter decreases.
- BThe weight of the matter does not change.
- CThe weight of the matter increases.
- DThe gas in the balloon will have no net weight since helium defies gravity and vertically rises.
- EWeight will stay the same since only gases are filling it.

**Q9: **

An astronaut with a mass of 55 kg is in a spacecraft that is traveling around Earth at a constant speed , as shown in the diagram. The gravitational field strength of Earth inside the spacecraft is 9.6 N/kg.

What is the magnitude of the force that the astronaut feels acting toward the side of the spacecraft with which her feet are in contact?

What is the magnitude of the force on the astronaut acting toward the side of the spacecraft perpendicular to the side with which her feet are in contact (the side facing Earth)?

**Q10: **

An astronaut with a mass of 50 kg is in a spacecraft that is traveling around Earth at a constant speed , as shown in the diagram. The gravitational field strength of the earth inside the spacecraft is 9.7 N/kg. The astronaut’s feet are in contact with a wall of the spacecraft, the center of which is perpendicular to a point on the surface of Earth directly below it. The astronaut’s feet are equidistant from a point at the center of the wall that he stands on.

What is the weight of the astronaut?

What force do the astronaut’s feet exert on the wall of the spacecraft that they are in contact with?