2. Signs often caution you to slow your car
down before you come to a sharp turn. That's because your car is
more likely to skid during the turn when it's moving fast. Why
is skidding more likely when you make a turn at high
speed?
During a turn, inertia causes your car to try to continue moving
along in the direction it is currently traveling (rather than
around the curve). A particular amount of force, directed toward
the geometric center of the arc forming the turn, is needed to
turn the car's velocity vector while maintaining constant speed.
This force is called the centripetal force. It is proportional
to the square of the car's linear speed and inversely
proportional to the radius of the curve. The faster your car is
moving, the more centripetal force is needed.
Physically, friction between the tires and the road produce the
centripetal force. But static friction has an upper limit given
by the normal force of the road on the car, multiplied by the
coefficient of static friction. If your speed requires a larger
centripetal force than can be supplied by friction, you begin to
skid!
8. Some decorative light bulbs have a loop-shaped filament that jitters back and forth near a small
permanent magnet. When electric charge moves through the
filament, it's attracted to or repelled by the magnet. The
filament wire itself isn't magnetic, so why does the permanent
magnet push or pull on the filament when the light is turned
on?
Electric current moving through the filament heats the wire and
causes it to glow. This current is made up of moving electric
charges. Individually, each moving charge experiences a force
due to its motion through the magnetic field of the permanent
magnet. The direction of this force depends on the direction of
the magnetic field, and the direction of current flow. So, the
force reverses direction each time the current does, for a light
bulb connected to alternating current.
Still, the electric charges that make up the current are confined
inside the non-magnetic wire. As they move along, they try to
move in the direction of the magnetic force but cannot do so when
they hit the boundary of the filament. They push against the
wire and cause it to move. The motion appears to be jittering
back and forth because the direction that the charges push
against the wire reverses at the frequency of the alternating
current, which is 60 cycles per second in the US.
10. You can probably balance a long pole on
your hand, but only if you're allowed to watch it. If you close
your eyes, it's certain to fall. Why?
The pole balanced on your hand is in unstable equilibrium. That
means it will not return to it's equilibrium position if it
wanders off that position even a small amount, and so will fall.
If you can't watch the pole, you can't see any changes in its
position and move it back to equilibrium. You need to be able to
see the pole and actively adjust your hand to keep it in unstable
equilibrium.
14. One of the ways in which a coin operated
vending machine checks to make sure that the coins you feed it
are genuine is to roll them past a strong magnet. Why do coins
made of good electric conductors such as copper slow down as they
pass the magnet?
The coin rolling past the magnet is moving the electric charges
inside it past the magnet as well, as some kind of speed. These
moving charges feel a force due to the magnet and begin to move
as a current inside the coin. But, a moving current in a regular
conductor is subject to a resistance to its motion, due to the
specific material making up the conductor. This resistance
causes some of the electrical energy of the current to be
transformed into heat. Conservation of energy tells us that all
of the energy involved in this process had to come from
somewhere. In this case, the source is the kinetic energy of the
rolling coin. So the coin's kinetic energy is reduced and the
coin slows down when it passes by the magnet.
18. If you move a permanent magnet across a
piece of copper, you will induce currents in that copper. If you
try the same with a piece of glass, no currents will flow. Why
don't currents flow in the glass as the magnet moves
by?
The electric charges in the piece of copper experience the change
in the magnetic field and are subject to a force, just as if the
magnet was being held still and the piece of copper moved. Since
copper is a good conductor, the electrons are able to move in
response to this magnetic force that is induced and produce a
current.
Glass is an insulator and not a good conductor. The electric
charges in the piece of glass also experience the induced
magnetic force, but they are not free to move within the glass
and cannot produce a current.
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