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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.