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452 CHAPTER 14 Statics and Elasticity

7. A carpenter wants to support the (flat) roof of a building with 8. The long bones in the limbs of vertebrates have the shape of
horizontal beams of wood of rectangular cross section. To hollow pipes. If the same amount of bone tissue had been
achieve maximum strength of the roof (least sag), should he assembled in a solid rod (of correspondingly smaller cross
install the beams with their narrow side up or with their wide section), would the limb have been more rigid or less rigid?
side up?

PROBLEMS

4.2 Examples of Static Equilibrium 3. Consider the bridge with the locomotive described in
Example 1 and suppose that, besides the first locomotive at
1. At a construction site, a laborer pushes horizontally against a
30 m from the right end, there is a second locomotive, also of
large bucket full of concrete of total mass 600 kg suspended
90000 kg, at 80 m from the right end. What is the load on
from a crane by a 20-m cable (see Fig. 14.32). What is the
each pier in this case?
force the laborer has to exert to hold the bucket at a distance
4. Repeat the calculations of Example 1 assuming that the bridge
of 2.0 m from the vertical?
has a slope of 1:7, with the left end higher than the right.
5. In order to pull an automobile out of the mud in which it is
stuck, the driver stretches a rope taut from the front end of
the automobile to a stout tree. He then pushes sideways
against the rope at the midpoint (see Fig. 14.34). When he
pushes with a force of 900 N, the angle between the two
halves of the rope on his right and left is 170 . What is the
tension in the rope under these conditions?
6. A mountaineer is trying to cross a crevasse by means of a rope
stretched from one side to the other (see Fig. 14.35). The
mass of the mountaineer is 90 kg. If the two parts of the rope
make angles of 40 and 20 with the horizontal, what are the
tensions in the two parts?
FIGURE 14.32
Bucket hanging
from a cable.
40° 20°
2. You are holding a meterstick of 0.20 kg horizontally in one
hand. Assume that your hand is wrapped around the last
10 cm of the stick (see Fig. 14.33), so the front edge of your
hand exerts an upward force and the rear edge of your hand
exerts a downward force. Calculate these forces.

FIGURE 14.33 A meterstick held in a hand. FIGURE 14.35 Mountaineer suspended from a rope.

FIGURE 14.34 The rope is
stretched between the automobile
and a tree. The driver is pushing
at the midpoint.