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More general combinations of forces
It is too constraining to restrict our attention to cases where all the
forces lie along the line of the center of mass’s motion. For one thing, we
can’t analyze any case of horizontal motion, since any object on earth will be
subject to a vertical gravitational force! For instance, when you are driving
your car down a straight road, there are both horizontal forces and vertical
forces. However, the vertical forces have no effect on the center of mass
motion, because the road’s upward force simply counteracts the earth’s
downward gravitational force and keeps the car from sinking into the
ground.
Later in the book we’ll deal with the most general case of many forces
acting on an object at any angles, using the mathematical technique of
vector addition, but the following slight generalization of Newton’s first law
allows us to analyze a great many cases of interest:
Suppose that an object has two sets of forces acting on it, one set along
the line of the object’s initial motion and another set perpendicular to
the first set. If both sets of forces cancel, then the object’s center of mass
continues in the same state of motion.
Example: a car crash
Question: If you drive your car into a brick wall, what is the
mysterious force that slams your face into the steering wheel.
Answer: Your surgeon has taken physics, so she is not going to
believe your claim that a mysterious force is to blame. She
knows that your face was just following Newton’s first law.
Immediately after your car hit the wall, the only forces acting on
your head were the same canceling-out forces that had existed
previously: the earth’s downward gravitational force and the
upward force from your neck. There were no forward or
backward forces on your head, but the car did experience a
backward force from the wall, so the car slowed down and your
face caught up.
Example: a passenger riding the subway
Question: Describe the forces acting on a person standing in a
subway train that is cruising at constant velocity.
Answer: No force is necessary to keep the person moving
relative to the ground. He will not be swept to the back of the
train if the floor is slippery. There are two vertical forces on him,
the earth’s downward gravitational force and the floor’s upward
force, which cancel. There are no horizontal forces on him at all,
so of course the total horizontal force is zero.
Example: forces on a sailboat
Question: If a sailboat is cruising at constant velocity with the
wind coming from directly behind it, what must be true about the
forces acting on it.
Answer: The forces acting on the boat must be canceling each
other out. The boat is not sinking or leaping into the air, so
evidently the vertical forces are canceling out. The vertical forces
are the downward gravitational force exerted by the planet earth
and an upward force from the water.
The air is making a forward force on the sail, and if the boat
is not accelerating horizontally then the water’s backward
water's frictional
force on boat
air's force
on sail
water's bouyant
force on boat
earth's gravitational
force on boat
Chapter 4Force and Motion