2. Some shoes have lights that flash with
every step. These lights are triggered by a drop of liquid that
moves inside the shoe. Which way does the liquid travel within
the shoe when the shoe suddenly stops moving
forward?
Just before the shoe stops moving forward, the shoe and
everything inside it were moving uniformly forward. When you
cause the shoe to stop, the inertia of the liquid causes it to
continue moving forward until other forces act on it.
4. As you jump across a small stream, does a
horizontal force keep you moving forward? If so, what is the
force?
There is no horizontal force acting to move you forward, it is
your inertia continuing you forward since you were already headed
that way.
8. Why is it so difficult to start moving
forward or come to a stop when you are wearing roller skates on
your feet?
The easily-turning wheels on roller skates make us ineffective in
exerting horizontal forces on the surrounding environment. So,
our motion is determined by the principle of inertia. This says
that, in the absence of unbalanced external forces, we remain in
our current state of uniform motion - either stopped or rolling
along at constant speed.
10. Why is your velocity constantly changing
as you ride on a carousel?
When your velocity is constant, inertia causes you to travel
along a straight line. On a carousel, you are traveling around
on a circle. So, the direction of your velocity is constantly
changing just enough to keep you on that circular path, even
though your speed (which is the magnitude, or size, of your
velocity) is constant.
12. A ball falls from rest for 5 seconds.
Neglecting air resistance, during which of the 5 seconds does the
ball's speed increase most?
Near the earth's surface, the force of gravity on an object is
what we usually call its weight. The weight of an object is the
same whether it is falling or standing still, because it is the
pull (attractive force) that the earth exerts on it. Newton's
second law relates the force on an object to its acceleration,
F=ma. So, the ball has a constant acceleration the whole time it
is falling as long as we can neglect air resistance. But
acceleration is defined as the change in an object's velocity
divided by the time for that change to occur. If we look at 1
second time intervals during the ball's fall, the change in its
speed must be the same for each 1 second interval because its
acceleration is constant. Note that we are able to talk about
velocity and speed interchangeably here because the direction
associated with this speed is always the same, downward.
16. An acorn falls from a branch located 9.8
m above the ground. After 1 second of falling, the acorn's
velocity will be 9.8 m/s downward. Why hasn't the acorn hit the
ground?
The acorn's instantaneous speed is 9.8 m/s at the end of 1
second, but it has been falling slower than that until the 1
second mark. Its starting speed was zero at the time it began to
fall, and it accelerates at a constant rate of 9.8 m/s/s. Its
average speed during the first second of its fall is one-half of
its starting and ending speeds, or 4.9 m/s. So, it has only
dropped a distance of 4.9 m during that first second.
22. In the movies, rooftop chases often
involve death defying leaps from one building to another. If the
two rooftops are at the same height, why must the leaper jump
upward in order to cross the gap successfully?
From the instant that the leaper begins to cross between
rooftops, the person is falling vertically under the force of
gravity. It will take a certain amount of time for the leaper to
cross the horizontal gap, and they will fall a vertical distance
given by the acceleration of gravity acting downward for that
amount of time (evaluated in the distance equation). If they
don't jump appropriately upward, the leaper will be below the
level of the next rooftop by the time they reach it! The upward
speed must provide at least the same distance as the fall under
gravity during the rooftop crossing time.
24. If you drive down an icy road and slam
on the brakes, your car will begin to slide. If the road is
straight, your car will stay on it but if the road curves, your
car may end up in a ditch. Why does the road's shape determine
whether you stay on it or not?
When you slam on your brakes while sliding down an icy road, your
vehicle begins to skid and inertia has your vehicle continuing
along its straight line path at constant speed during the skid.
When sliding on very smooth ice, the friction force you use to
change your vehicle's path (accelerate) is essentially gone. If
the road is quite straight, then your path carries you along the
road provided you were traveling straight ahead as you began the
skid. But if the road curves to either side, your vehicle will
continue its straight line path right into a ditch.
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