Describing Motion

The Physical World

Robert Lambourne

• Publisher: CRC Press
• Year: 2019
• eBook ISBN: 9780429529894
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Describing Motion: The Physical World provides the quantitative description of a variety of physically important motions. Starting with simple examples of motion along a line, the book introduces key concepts, such as position, velocity, and acceleration, using the fundamental rules of differential calculus. Topics include the free-fall motion of m

Chapter 1 Motion along a line

1 From drop-towers to Oblivion — some applications of linear motion

We have all experienced that momentary feeling of lightness when an elevator begins its downward motion. It is almost as if our weight had suddenly been reduced or, conceivably, that the pull of the Earth’s gravity had decreased for a moment. But imagine what it would be like if the lift cable had suddenly snapped and the lift, with you in it, had plummeted downward. Apart from stark terror, what else do you think you would experience during your fall? What would the physical experience of such a disaster be like?

Well, it would be just like jumping from a high tower. If your descent was unimpeded by the resistance of the air, almost all sense of weight would vanish while you were falling. You would feel weightless, just as though you were an astronaut in outer space.

Not surprisingly, scientists who want to know how equipment will behave under the conditions found in spacecraft are keen to simulate the same conditions here on Earth. One way in which they can do this is by dropping their equipment from the top of a tower, or down a vertical shaft. There are a number of research centres around the world where drop facilities of this kind are available. These are specialized facilities where steps are taken to avoid or overcome the effects of air resistance: simply dropping an object in the Earth’s atmosphere is not a satisfactory way of simulating the environment of outer space.

Figure 1.1 The 140m drop-tower in Bremen, Germany.

Figure 1.1 shows the 140 m drop-tower in Bremen, Germany. The tower is airtight, so all the air can be pumped out. Equipment under test is placed inside a specially constructed drop-vehicle and monitored by closed-circuit TV as it falls from the top to the bottom of the tower. About five seconds of free fall can be achieved in this way. During those few seconds, within the falling drop-vehicle, the effects of gravity are reduced to a tiny fraction of their usual value, a condition known as ‘microgravity’.

In the USA, at the Lewis Research Center in Ohio, NASA operates a 143 m drop-shaft, as part of its Zero Gravity Research Facility. Microgravity investigations conducted at the research facility have concerned the spread of fire, the flow of liquids, and the feasibility of space-based industrial processes that would be impossible under normal terrestrial conditions. Figure 1.2 shows the facility’s bullet-shaped drop-vehicle being given a soft landing at the end of a drop, to avoid destroying the expensive equipment that it contains.

At the time of writing, the world’s longest drop-shaft is in Japan. The Japan Microgravity Center (JAMIC) has a 700 m drop housed in a disused mine shaft. It would be impossible to evacuate the air from such a big shaft, so in this case the rocket-shaped test capsule is propelled down the shaft by gas-jets with a thrust that is designed to compensate for air resistance. Inside this capsule, there is a second capsule and the space between the capsules is a vacuum. The experiments are carried out in the inner capsule which, to a very good approximation, is in free fall. The two capsules decelerate during the final 200 m of the fall.

Figure 1.2 The linear motion of a falling test vehicle is stopped safely at the NASA Lewis Zero Gravity Research Facility in Ohio, USA.

By the time you finish this chapter you should be able to work out the duration of the fall in the JAMIC facility, and the highest speed attained by the capsule. You should also be able to work out the length of shaft that would be required to produce any given duration of microgravity.

If all this sounds a bit esoteric you might prefer to consider a different kind of drop-facility. Figure 1.3 shows Oblivion, a ride at the Alton Towers Adventure Park, UK. Oblivion is described as ‘the world’s first vertical-drop roller-coaster’. It will not simulate the space environment, but it will produce a few seconds of terror from a simple application of linear motion.

Figure 1.3 Oblivion, the vertical-drop roller-coaster at the Alton Towers Adventure Park, UK.

2 Positions along a line

2.1 Simplification and modelling

Everyday experience teaches us that unconfined objects are free to move in three independent directions. I can move my hand up or down, left or right, backwards or forwards. By combining movements in these three directions I can, at least in principle, move my hand to any point in space. The fact that there are just three independent directions, and that these suffice to reach any point, shows that the space in which my hand moves is three-dimensional.

The motion of a large object, such as an aeroplane, moving in three-dimensional spa...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• Chapter 1 Motion along a line
• 2 Motion in a plane and in space
• Chapter 3 Periodic motion
• Chapter 4 Consolidation and skills development
• Answers and comments
• Acknowledgements
• Index