Physics: Principles and Problems
9th Edition
ISBN: 9780078458132
Table of contents
Textbook solutions
All Solutions
Page 217: Section Review
Exercise 40
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Yes it is possible for the centre of mass to be located in an area where the object has no mass
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Two examples are shown below :
Exercise 41
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The car becomes less stable because the center of mass becomes higher. The inertia forces act in the center of mass, and, because the center of mass is now higher, the torque caused by those forces is now bigger due to having a longer lever in respect to the pivot point which is the floor.
Result
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Higher center of the mass causes higher torque due to inertial forces.
Exercise 42
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a) First example could be a $textbf{canon ball}$ which is not rotating because the sum of all torque on it is equal to zero, but is deaccelerating due to the force of drag.
b) Second equation could be a $textbf{motor axle}$, which is not translating anywhere because the sum of all forces acting on it is equal to zero, but is spinning faster and faster due to the torque acting on it.
Result
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a) Canon ball
b) Motor axle
Exercise 43
Solution 1
Solution 2
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The center of mass of the masking tape is found in the middle, open space of the tape roll.
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The roll of masking tape is a thin hoop of radius $r$. The center of a mass of an object can be determined by suspending the object on various points and drawing the lines from the suspension point. Where the lines cross, that is the place of the center of the mass. Two lines are enough to determine the center of the mass.
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If we suspend the roll of tape and draw the first line, the diagram looks like this:
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Since we need another line, we suspend the roll of tape from another point:
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Crossing both of the lines we get that they cross exactly in the middle of the empty space of the rolling tape, as in the picture below:
Exercise 44
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Since we know that the only outside force acting on the book is its weight, we know that the book will reach $textbf{force and torque equilibrium}$ if the opposite force is put exactly at the spot where force of gravity is acting, which is its center of mass. This can easily be found by trying to balance a book on a single spot, when we reach the center of the mass, the book will be in equilibrium and the $textbf{pivot}$ on which the book rests will be marking the point where center of mass lays.
Result
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By balancing it on a single point
Exercise 45
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Penny left standing on the turntable will, due to the friction, start moving rotationally together with the record. As it is moving, centrifugal force will force it to the outern parts of the record. Or, better way to put it would be to say that lack of $textbf{centripetal force}$, which is directed inwards, will fail to change penny’s direction of velocity towards the inner parts and it will therefore, due to the $textbf{inertia}$, keep moving more towards a $textbf{straight line}$, which relative to the record seems as if its moving to the outern parts.
Exercise 46
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The winds would move in the opposite direction because winds coming from the north will move from the equator (where linear speed is the highest) to mid latitude (where linear speed is the lowest). Hence, the winds will bend to the east (in the opposite direction).
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