Problems from Arnold Arons' Book Homework and Test Questions for Introductory
Problem 3.40: Consider the situation
illustrated here: the system accelerates when object B is released. The
inertial effects of both the string and the pulley are negligible. The
string is essentially unstretchable.
Problem 9.9: Is it possible to connect two identical
batteries to make two bulbs in series light just as brightly as one alone
across one battery? If so, sketch and explain the circuit diagram. If not,
explain your reasoning.
How does the acceleration of body A compare with that of
body B? Are the accelerations equal or different? If different, which is
larger? Explain your reasoning.
While the system is accelerating, how does the magnitude
of the force exerted by the string on cart A compare with the weight of
body B? Is the force exerted by the string on cart A smaller than the weight
of body B? (An algebraic solution is not being called for; the reasoning
should performed quantitatively.) Explain your reasoning.
Suppose that mB is increased while mA
remains unchanged. What will happen to the acceleration of the system?
Will it increase, decrease, or remain unchanged? What will happen to the
force the string exerts on body A? What will happen as mB
is increased further and mA becomes very small relative
to mB ? Explain your reasoning.
Describe what will happen to the acceleration of the system
and to the force the string exerts on mA if the changes
in part (c) are reversed and mB becomes very small relative
to mA. Explain your reasoning.
Suppose carts A and B are connected by a rope with significant
mass rather than by a massless string. Will the acceleration of the system
be uniform or nonuniform? If nonuniform, will the acceleration increase
or decrease after release of cart B? Explain your reasoning.
What difficulties would be introduced into the problem if
the string or rope connecting the two bodies were stretchable rather than
Problem 9.11: You have heard the term "short circuit"
used in a variety of circumstances. Define this term operationally.
(This means that you must describe actions and observations of results
of these actions. Words or synonyms alone are not adequate.)