4. Why does less snow and other debris
accumulate on a steep roof than on a shallow roof?
When snow or debris sits on a roof, it is the component of the
object's weight parallel to the roof that can cause it to slide
off. The component of its weight perpendicular to the roof is
cancelled out by the normal force of the roof on the debris (that
keeps it from falling through the roof). If a roof is shallow,
more of the object's weight is in the component perpendicular to
the roof. With a steep roof, the component of its weight
parallel to the roof is greater, causing it to slide off the roof
more frequently.
6. You roll a marble down a playground slide
that starts level, then curves downward, and finally curves very
gradually upward so that it's level again at the end. Where
along its travel is the marble undergoing the largest
acceleration?
The only relevant force acting on the marble to produce an
acceleration is its weight, the force of gravity that the earth
exerts on it. The marble's acceleration will be greatest when
the component of its weight parallel to the slide is greatest,
since the component of its weight perpendicular to the slide is
just cancelled by the normal force exerted on the marble by the
slide. The parallel component of the marble's weight will be
greatest somewhere in the middle section of the slide, where the
downward slope of the slide is the greatest.
12. A speedboat is pulling a water-skier
with a rope, exerting a large forward force on her. The skier is
traveling forward in a straight line at constant speed. What is
the net force she experiences?
We know that the skier is traveling in a straight line at
constant speed. Thinking about this with Newton's 1st and 2nd
laws tells us that the skier is experiencing zero net force, or
her acceleration would be nonzero and her velocity changing in
size or direction.
14. A car passes by, heading to your left,
and you reach out and push it toward the left with a force of 50
N. Does this moving car push on you and, if so, with what
force?
When you push to the left on the passing car with a force of 50
N, it pushes back on you with a force of 50 N to the right. We
know this since Newton's 3rd law requires an equal and opposite
reaction force to be exerted on you by the other car.
20. You accidentally miss the doorway and
run into the wall. You suddenly experience a backward force that
is several times larger than your weight. What's the origin of
this force?
The force that you experience when you run into the wall and
doorframe is equal and opposite to the force you exert on these
objects when you contact them, following the prescription in
Newton's 3rd law. This force originates in the normal force
exerted by the surfaces of these objects on you to keep you from
passing through the wall when you hit it; the force acts at a
minimum to decelerate you and stop your forward motion. (At a
more fundamental level, this force originates in the electric
forces between the atoms of the wall and the atoms that make up
your body.)
22. You're cutting wood with a hand saw.
You have to push the saw away from you as it moves away from you
and pull the saw toward you as it moves toward you. When are you
doing work on the saw?
You are doing work on the saw during both motions but not at the
ends of the motion when the saw briefly stops moving. In both
directions, the force you exert is in the direction of the motion
so the work done (defined as the product of the force parallel to
the motion with the distance traveled) is positive in both
instances.
28. When you're roller skating on level
pavement, you can maintain your speed for a long time. But as
soon as you start up a gradual hill, you begin to slow down.
What slows you?
As you start up a hill, a component of your weight is not
cancelled by the normal force of the pavement. This component of
force is directed opposite (anti-parallel) to your direction of
travel up the hill and acts to slow you down. The work done on
you by this force is negative, so it reduces your kinetic energy
(energy of motion). The amount of decrease in kinetic energy is
equal to the amount of increase in gravitational potential
energy, as long as friction can be ignored.
32. Why does tapping your toothbrush on the
sink dry it off?
Just before your toothbrush contacts the sink, the toothbrush and
the water on it are moving at high speed toward the sink. When
the toothbrush hits the sink, it reverses direction and moves
away from the sink at high speed. (We will learn more about this
property of elastic collisions later.) But, the inertia of the
water on the toothbrush keeps it moving toward the sink since
there are no strong forces causing it to change its motion; the
friction forces between the water and the toothbrush are not
large. In the end, the water falls off the toothbrush when each
has moved far enough to no longer be in contact with each other.
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