g/A swimmer doing the breast
stroke pushes backward against
the water. By Newton’s third law,
the water pushes forward on him.h/A coin slides across a ta-
ble. Even for motion in one
dimension, some of the forces
may not lie along the line of the
motion.x(m) t(s)
10 1.84
20 2.86
30 3.80
40 4.67
50 5.53
60 6.38
70 7.23
80 8.10
90 8.96
100 9.83
Discussion question B.There is, however, a complication with force that we were able
to avoid with momentum. If an object is moving on a line, we’re
guaranteed that its momentum is in one of two directions: the two
directions along the line. But even an object that stays on a line
may still be subject to forces that act perpendicularly to the line.
For example, suppose a coin is sliding to the right across a table, h,
and let’s choose a positivexaxis that points to the right. The coin’s
motion is along a horizontal line, and its momentum is positive and
decreasing. Because the momentum is decreasing, its time derivative
dp/dtis negative. This derivative equals the horizontal force of
frictionF 1 , and its negative sign tells us that this force on the coin
is to the left.
But there are also vertical forces on the coin. The Earth exerts
a downward gravitational forceF 2 on it, and the table makes an
upward forceF 3 that prevents the coin from sinking into the wood.
In fact, without these vertical forces the horizontal frictional force
wouldn’t exist: surfaces don’t exert friction against one another
unless they are being pressed together.
To avoid mathematical complication, we want to postpone the
full three-dimensional treatment of force and momentum until sec-
tion 3.4. For now, we’ll limit ourselves to examples like the coin, in
which the motion is confined to a line, and any forces perpendicular
to the line cancel each other out.
Discussion Questions
A Criticize the following incorrect statement:
“If an object is at rest and the total force on it is zero, it stays at rest.
There can also be cases where an object is moving and keeps on moving
without having any total force on it, but that can only happen when there’s
no friction, like in outer space.”
B The table gives laser timing data for Ben Johnson’s 100 m dash at the
1987 World Championship in Rome. (His world record was later revoked
because he tested positive for steroids.) How does the total force on him
change over the duration of the race?
C You hit a tennis ball against a wall. Explain any and all incorrect
ideas in the following description of the physics involved: “According to
Newton’s third law, there has to be a force opposite to your force on the
ball. The opposite force is the ball’s mass, which resists acceleration, and
also air resistance.”
D Tam Anh grabs Sarah by the hand and tries to pull her. She tries
to remain standing without moving. A student analyzes the situation as
follows. “If Tam Anh’s force on Sarah is greater than her force on him,
he can get her to move. Otherwise, she’ll be able to stay where she is.”
What’s wrong with this analysis?
3.2.3 What force is not
Violin teachers have to endure their beginning students’ screech-
ing. A frown appears on the woodwind teacher’s face as she watchesSection 3.2 Force in one dimension 153