2. Some amusement park rides move you back
and forth in a horizontal direction. Why is this motion so much
more disturbing to your body than cruising at a high speed in a
jet airplane?
Moving back and forth horizontally exerts a horizontal force on
your body whenever your speed or direction changes. This adds
(as a vector) with your weight, appreciably changing your
apparent weight. On the other hand, cruising along smoothly in a
jet at a high but constant speed does nothing to change your
apparent weight.
8. A hammer's weight is downward, so how can
a hammer push a nail upward into the ceiling?
It is true that a hammer's weight is always downward, as is that
of a nail. But, the force that drives a nail upward into a
ceiling is part of the Newton's 3rd Law action-reaction pair
arising from its collision with the hammer. First, you supply
the force causing the hammer to move sharply upward against its
weight. When it hits the nail, a pair of interaction forces
arise because the hammer does not pass through the nail but
rebounds from it at collision. That is, the nail exerts a
downward force on the hammer sufficient to change its upward
speed in a very short time. The nail experiences an equally
strong, but upward, force simultaneously. This upward force
pushes the nail into the ceiling.
10. Some amusement park rides swing you all
the way upside down in a circle. Suppose that you're in one of
these rides and that as the ride swings you over the top, your
head is nearer to the ground than your feet are. If the ride
goes over the top of the circle quickly, your hat stays on and
you can hardly tell that you're upside down. But if the ride
goes over the top slowly, your hat falls off and objects come out
of your shirt pocket. What causes these different
behaviors?
When the ride goes over the top of the circle slowly, the
downward force of gravity on the hat accelerates it downward
faster than your downward acceleration in the ride. Then, the
hat travels a greater vertical distance downward in a given time
than you do, and it falls off.
But if the ride goes fast enough over the top, your downward
acceleration is greater than that of gravity. Then, your head
exerts an additional downward force on the hat to get it to
accelerate just as quickly as you. When this happens, your
downward acceleration is exactly the same as that of the hat, so
you travel equal downward distances in equal times. Your hat
then stays on your head since you are moving equally.
12. Why do skiers begin to skid across the
snow when they try to turn too sharply?
Much of the force that allows a skier to turn in spite of their
inertia when on snow is friction. The ski and edges experience a
certain amount of friction in a direction at right angles to the
skier's travel and the snow exerts a Newton's 3rd law reaction
force on the ski. This force, when controlled by the skier,
produces a turn. Note that the friction force is in a direction
for which the ski is NOT moving, so it is static friction. But
there is an upper limit to the amount of static friction force
that can exist between two surfaces, depending on the type of
surface, the contact area, and the normal force involved. When
the skier's turn is very sharp, it requires a greater force than
static friction can supply. Once the static friction limit is
passed, the ski begins to slide under kinetic friction which can
only exert a smaller force than static friction.
18. Why do trains have brakes on each car,
rather than just on the locomotive?
Braking force is supplied by the friction of contact between
surfaces. This includes the contact between surfaces within the
brakes and the contact friction between the wheels and the rails.
If a train had brakes only on the locomotive, all of the stopping
force for the train would be supplied by friction at the
locomotive alone! Given the upper limit that exists for static
friction and the limited strength of materials that we use, the
stopping force available for the train could only provide a
certain, small amount of deceleration. To be able to stop the
train more quickly, the frictional stopping force must be
distributed among more cars on the train. Putting brakes on
every car does this ideally. Since the static friction limit
depends on the normal force (or equivalently the weight in this
case) of a given train car, a braking force proportional to each
car's weight can be used to slow the train very evenly and reduce
strain on the couplings.
22. People falling from a high diving board
feel weightless. Has gravity stopped exerting a force on them?
If not, why don't they feel it?
Gravity exerts a force on them all the time. But we experience
weight in terms of the forces exerted on us that act to oppose
the force of gravity. Since they are falling from the high board
with an acceleration equal to that of gravity, the force acting
to oppose gravity must be zero. They feel no apparent
weight.
24. As your car reaches the top in a
smoothly turning Ferris wheel, which way are you
accelerating?
You move around a circle at constant speed in a smoothly moving
Ferris wheel. The centripetal acceleration you experience in
this uniform circular motion is directly toward the center of the
circle, or Ferris wheel. We know this because the acceleration
does not cause your motion to speed up or slow down, only to
change direction around the circle.
26. Astronauts learn to tolerate large g's
by riding in a huge centrifuge. An astronaut's apparent weight
depends on both the size of the centrifuge and on how quickly it
turns. Explain.
The astronaut's apparent weight is determined by the centripetal
force experienced in the centrifuge. The centripetal force
increases with the square of the centrifuge's speed and decreases
linearly with the length of the centrifuge arm. When the linear
speed is reinterpreted in terms of angular speed instead, the
centripetal force increases with the square of the angular speed
and increases linearly with centrifuge arm length. (Recall that
linear speed around the circle is equal to the product of the
angular speed and the arm length.)
28. What keeps the ball pressed against the
outside rim of a spinning roulette wheel? Why does the ball roll
inward off the rim as the wheel slows down?
The ball's inertia keeps it on the outside rim of the wheel when
it is spinning quickly. The component of the ball's weight that
is parallel to the roulette wheel's surface (directed toward the
wheel's center) is less than the centripetal force required by
the speed of the ball and its distance from the wheel's center.
As the wheel slows, the ball's speed slows and the required
centripetal force decreases. The surface-directed component of
its weight then exceeds the value of the centripetal force and
the ball begins moving inward. (Remember that the calculated
centripetal force tells us the magnitude of force required to
maintain a circular orbit of constant radius and constant
speed.)
32. A rodeo rider must hold tight to a
bucking bull to avoid being thrown off. The bull contorts its
body so that its back accelerates downward faster than the
acceleration due to gravity. Why does that movement tend to lose
the rider?
The rider moves upward with the bull because of the upward force
exerted on the rider by the bull. But when the bull accelerates
downward, the downward force on the rider is largely supplied by
the rider's own weight. The rider's downward acceleration is
that of gravity, while the bull's downward acceleration exceeds
that of gravity and leaves the rider behind.
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