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only necessary for speeding the car up when it starts going up or
slowing it down when it finishes going down. Decreased force is
needed to speed the car up when it gets going down and to slow
it down when it finishes going up. But when the elevator is
cruising at constant velocity, Newton’s first law says that you just
need to cancel the force of the earth’s gravity.
To many students, the statement in the example that the cable’s upward
force “cancels” the earth’s downward gravitational force implies that there
has been a contest, and the cable’s force has won, vanquishing the earth’s
gravitational force and making it disappear. That is incorrect. Both forces
continue to exist, but because they add up numerically to zero, the elevator
has no center-of-mass acceleration. We know that both forces continue to
exist because they both have side-effects other than their effects on the car’s
center-of-mass motion. The force acting between the cable and the car
continues to produce tension in the cable and keep the cable taut. The
earth’s gravitational force continues to keep the passengers (whom we are
considering as part of the elevator-object) stuck to the floor and to produce
internal stresses in the walls of the car, which must hold up the floor.
Example: terminal velocity for falling objects
Question: An object like a feather that is not dense or
streamlined does not fall with constant acceleration, because air
resistance is nonnegligible. In fact, its acceleration tapers off to
nearly zero within a fraction of a second, and the feather finishes
dropping at constant speed (known as its terminal velocity). Why
does this happen.
Answer: Newton’s first law tells us that the total force on the
feather must have been reduced to nearly zero after a short time.
There are two forces acting on the feather: a downward
gravitational force from the planet earth, and an upward frictional
force from the air. As the feather speeds up, the air friction
becomes stronger and stronger, and eventually it cancels out the
earth’s gravitational force, so the feather just continues with
constant velocity without speeding up any more.
The situation for a skydiver is exactly analogous. It’s just that
the skydiver experiences perhaps a million times more
gravitational force than the feather, and it is not until she is falling
very fast that the force of air friction becomes as strong as the
gravitational force. It takes her several seconds to reach terminal
velocity, which is on the order of a hundred miles per hour.
Section 4.2Newton’s First Law