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Problem 17.
16 S. (a) Using the solution of problem 14, which is given in the back of
the book, predict how the spring constant of a fiber will depend on its
length and cross-sectional area. (b) The constant of proportionality is
called the Young’s modulus, E, and typical values of the Young’s modulus
are about 10
10
to 10
11
. What units would the Young’s modulus have in the
SI (meter-kilogram-second) system.
17. This problem depends on the results of problems 14 and 16, whose
solutions are in the back of the book. When atoms form chemical bonds,
it makes sense to talk about the spring constant of the bond as a measure
of how “stiff” it is. Of course, there aren’t really little springs — this is just
a mechanical model. The purpose of this problem is to estimate the spring
constant, k, for a single bond in a typical piece of solid matter. Suppose we
have a fiber, like a hair or a piece of fishing line, and imagine for simplicity
that it is made of atoms of a single element stacked in a cubical manner, as
shown in the figure, with a center-to-center spacing b. A typical value for b
would be about 10
–10
m. (a) Find an equation for k in terms of b, and in
terms of the Young’s modulus, E, defined in problem 16 and its solution.
(b) Estimate k using the numerical data given in problem 16. (c) Suppose
you could grab one of the atoms in a diatomic molecule like H
2
or O
2
,
and let the other atom hang vertically below it. Does the bond stretch by
any appreciable fraction due to gravity.
18 S. In each case, identify the force that causes the acceleration, and give
its Newton’s-third-law partner. Describe the effect of the partner force. (a)
A swimmer speeds up. (b) A golfer hits the ball off of the tee. (c) An archer
fires an arrow. (d) A locomotive slows down.
19. Ginny has a plan. She is going to ride her sled while her dog Foo pulls
her. However, Ginny hasn’t taken physics, so there may be a problem: she
may slide right off the sled when Foo starts pulling. (a) Analyze all the
forces in which Giny participates, making a table as in section 5.3. (b)
Analyze all the forces in which the sled participates. (c) The sled has
mass m, and Ginny has mass M. The coefficient of static friction between
the sled and the snow is
µ
1
, and
µ
2
is the corresponding quantity for static
friction between the sled and her snow pants. Ginny must have a certain
minimum mass so that she will not slip off the sled. Find this in terms of
the other three variables.(d) Under what conditions will there be no
solution for M.
20 S. The second example in section 5.1 involves a person pushing a box
up a hill. The incorrect answer describes three forces. For each of these
three forces, give the force that it is related to by Newton’s third law, and
state the type of force.
21. The example in section 5.6 describes a force-doubling setup involving
a pulley. Make up a more complicated arrangement, using more than one
pullry, that would multiply the force by a factor greater than two.
22. Pick up a heavy object such as a backpack or a chair, and stand on a
bathroom scale. Shake the object up and down. What do you observe.
Interpret your observations in terms of Newton’s third law.
23. A cop investigating the scene of an accident measures the length L of
a car’s skid marks in order to find out its speed v at the beginning of the
skid. Express v in terms of L and any other relevant variables.
Chapter 5Analysis of Forces
Problem 19.