Problemas de fisica

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12
Static Equilibrium and Elasticity
CHAPTER OUTLINE
12.1

The Conditions for
Equilibrium
More on the Center of
Gravity
Examples of Rigid Objects
in Static Equilibrium
Elastic Properties of Solids

ANSWERS TO QUESTIONS

12.3
12.4

Q12.1

When you bend over, your center of gravity shifts forward.
Once your CG is no longer over your feet, gravity contributes
to a nonzero nettorque on your body and you begin to rotate.

Q12.2

Yes, it can. Consider an object on a spring oscillating back and
forth. In the center of the motion both the sum of the torques
and the sum of the forces acting on the object are (separately)
zero. Again, a meteoroid flying freely through interstellar space
feels essentially no forces and keeps moving with constant
velocity.

Q12.312.2

No—one condition for equilibrium is that

∑ F = 0 . For this to

be true with only a single force acting on an object, that force
would have to be of zero magnitude; so really no forces act on
that object.
Q12.4

(a)

Consider pushing up with one hand on one side of a steering wheel and pulling down
equally hard with the other hand on the other side. A pair of equal-magnitudeoppositelydirected forces applied at different points is called a couple.

(b)

An object in free fall has a non-zero net force acting on it, but a net torque of zero about its
center of mass.

Q12.5

No. If the torques are all in the same direction, then the net torque cannot be zero.

Q12.6

(a)

Yes, provided that its angular momentum is constant.

(b)

Yes, provided that itslinear momentum is constant.

Q12.7

A V-shaped boomerang, a barstool, an empty coffee cup, a satellite dish, and a curving plastic slide
at the edge of a swimming pool each have a center of mass that is not within the bulk of the object.

Q12.8

Suspend the plywood from the nail, and hang the plumb bob from the nail. Trace on the plywood
along the string of the plumb bob. Now suspendthe plywood with the nail through a different point
on the plywood, not along the first line you drew. Again hang the plumb bob from the nail and trace
along the string. The center of gravity is located halfway through the thickness of the plywood
under the intersection of the two lines you drew.

349

350

Static Equilibrium and Elasticity

Q12.9

The center of gravity must bedirectly over the point where the chair leg contacts the floor. That
way, no torque is applied to the chair by gravity. The equilibrium is unstable.

Q12.10

She can be correct. If the dog stands on a relatively thick scale, the dog’s legs on the ground might
support more of its weight than its legs on the scale. She can check for and if necessary correct for
this error by having the dog standlike a bridge with two legs on the scale and two on a book of
equal thickness—a physics textbook is a good choice.

Q12.11

If their base areas are equal, the tall crate will topple first. Its center of gravity is higher off the incline
than that of the shorter crate. The taller crate can be rotated only through a smaller angle before its
center of gravity is no longer over its base.

Q12.12The free body diagram demonstrates that it is necessary to have
friction on the ground to counterbalance the normal force of the
wall and to keep the base of the ladder from sliding. Interestingly
enough, if there is friction on the floor and on the wall, it is not
possible to determine whether the ladder will slip from the
equilibrium conditions alone.

FIG. Q12.12
Q12.13

When youlift a load with your back, your back muscles must supply the torque not only to rotate
your upper body to a vertical position, but also to lift the load. Since the distance from the
pivot—your hips—to the load—essentially your shoulders—is great, the force required to supply
the lifting torque is very large. When lifting from your knees, your back muscles need only keep
your back straight....
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