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Chapter 4: Problem 31

Which person is weightless? (a) A child in the air as she plays on a trampoline. (b) A scuba diver exploring a deep-sea wreck. (c) An astronaut on the Moon.

Short Answer

Expert verified
The child in the air is weightless.

Step by step solution

01

Introduction of Concepts

Weightlessness occurs when only gravity influences an object's motion, with no external forces, like a surface pushing against it. This typically happens in free-fall.
02

Analyze the Child on a Trampoline

While a child is in the air, she experiences free-fall for a brief moment, as she is not in contact with any surface. During this time, gravity is the only force acting on her, thus she is weightless momentarily.
03

Consider the Scuba Diver

A scuba diver underwater is submerged in the ocean, which exerts buoyancy and drag forces on her body. These forces prevent the diver from being weightless.
04

Examine the Astronaut on the Moon

An astronaut on the Moon is in a gravitational field, and the Moon鈥檚 gravity pulls the astronaut towards its surface. Thus, the astronaut is not weightless, though they experience less weight due to the lower gravitational pull compared to Earth.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Free-Fall
Free-fall refers to a motion where an object is solely influenced by the force of gravity, without any interference from other forces like air resistance. In a free-fall situation, all objects experience what we describe as weightlessness. This is because they are not being supported by a surface, so there's no normal force acting on them.
Imagine you're jumping on a trampoline. At the highest point of your jump, you are momentarily in free-fall because only gravity is acting on you. This creates a sensation of weightlessness as you descend back down.
Key points to remember about free-fall:
  • Occurs when gravity is the sole force acting on an object.
  • Experienced by objects that are not in contact with any surface.
  • Provides a brief experience of weightlessness, like an astronaut in space.
Gravity
Gravity is the force of attraction between two masses. For us on Earth, it is what keeps our feet firmly on the ground and gives weight to objects. Every object with mass, no matter how big or small, exerts gravitational force.
On Earth, this gravitational pull is what gives us weight, calculated using the formula: \[ Weight = mass \times gravity \] Where gravity is approximately 9.8 m/s虏 on Earth.
Important aspects of gravity to consider:
  • It is a constant force that pulls objects toward the center of the mass.
  • It influences our sensation of weight and is vital for keeping celestial bodies in orbit.
  • Weight is the result of gravity acting on an object's mass.
Buoyancy
Buoyancy is the force that allows objects to float or sink in a fluid, such as water. It's crucial for understanding why objects behave differently in water versus air.
When a scuba diver is underwater, buoyancy acts to counteract gravity, giving the sensation of reduced weight or even weightlessness. However, since forces other than gravity are at play, the diver is not truly weightless. Buoyancy depends on the density of both the object and the fluid involved.
Here's what to remember about buoyancy:
  • It is an upward force exerted by a fluid, opposing gravity.
  • Determines whether an object floats, sinks or remains suspended.
  • Greater in more dense fluids, altering our sensation of weight underwater.
Moon Gravity
The Moon's gravity is much weaker than Earth's, approximately 1/6th of it. This difference allows astronauts to jump higher and carry heavy equipment more easily on the Moon than on Earth.
While the gravity on the Moon is less, it is not absent. Therefore, astronauts are not truly weightless; instead, they experience significantly reduced weight. This is why tasks and movements that require strength are much easier on the Moon.
Key considerations about Moon gravity:
  • Although weaker, it still exerts a gravitational pull on objects on the Moon.
  • Allows for reduced weight, enabling astronauts to perform activities more effortlessly.
  • Essential for lunar navigation and exploration as it affects movement and maneuverability.

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Most popular questions from this chapter

The Gravitational Law. a. How does quadrupling the distance between two objects affect the gravitational force between them? b. Suppose the Sun were somehow replaced by a star with twice as much mass. What would happen to the gravitational force between Earth and the Sun? c. Suppose Earth were moved to one-third of its current distance from the Sun. What would happen to the gravitational force between Earth and the Sun?

Elevator to Orbit. Some people have proposed building a giant elevator from Earth's surface to the altitude of geosynchronous orbit. The top of the elevator would then have the same orbital distance and period as any satellite in geosynchronous orbit. a. Suppose you were to let go of an object at the top of the elevator. Would the object fall? Would it orbit Earth? Explain. b. Briefly explain why (not counting the huge costs for construction) the elevator would make it much cheaper and easier to put satellites in orbit or to launch spacecraft into deep space.

Suppose you could enter a vacuum chamber (on Earth), that is, a chamber with no air in it. Inside this chamber, if you dropped a hammer and a feather from the same height at the same time, both would hit the bottom at the same time.

Explain why orbits cannot change spontancously. How can a gravitational encounter cause an orbit to change? How can an object achieve escape velocity?

Space Elevator. Read more about space elevators (see Problem 50 ) and how they might make it easier and cheaper to get to Earth orbit or beyond. Write a short report about the feasibility of building a space elevator, and briefly discuss the pros and cons of such a project.
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