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on each other. For instance, if we think of the two halves of the string as
two objects, then each half is exerting a force on the other half. If we
imagine the string as consisting of many small parts, then each segment is
transmitting a force to the next segment, and if the string has very little
mass, then all the forces are equal in magnitude. We refer to the magnitude
of the forces as the tension in the string, T. Although the tension is mea-
sured in units of Newtons, it is not itself a force. There are many forces
within the string, some in one direction and some in the other direction,
and their magnitudes are only approximately equal. The concept of tension
only makes sense as a general, approximate statement of how big all the
forces are.
If a rope goes over a pulley or around some other object, then the
tension throughout the rope is approximately equal so long as there is not
too much friction. A rod or stick can be treated in much the same way as a
string, but it is possible to have either compression or tension.
Since tension is not a type of force, the force exerted by a rope on some
other object must be of some definite type such as static friction, kinetic
friction, or a normal force. If you hold your dog’s leash with your hand
through the loop, then the force exerted by the leash on your hand is a
normal force: it is the force that keeps the leash from occupying the same
space as your hand. If you grasp a plain end of a rope, then the force
between the rope and your hand is a frictional force.
A more complex example of transmission of forces is the way a car
accelerates. Many people would describe the car’s engine as making the
force that accelerates the car, but the engine is part of the car, so that’s
impossible: objects can’t make forces on themselves. What really happens is
that the engine’s force is transmitted through the transmission to the axles,
then through the tires to the road. By Newton’s third law, there will thus be
a forward force from the road on the tires, which accelerates the car.
Discussion question
When you step on the gas pedal, is your foot’s force being transmitted in the
sense of the word used in this section.
5.5Objects Under Strain
A string lengthens slightly when you stretch it. Similarly, we have
already discussed how an apparently rigid object such as a wall is actually
flexing when it participates in a normal force. In other cases, the effect is
more obvious. A spring or a rubber band visibly elongates when stretched.
Common to all these examples is a change in shape of some kind:
lengthening, bending, compressing, etc. The change in shape can be
measured by picking some part of the object and measuring its position, x.
For concreteness, let’s imagine a spring with one end attached to a wall.
When no force is exerted, the unfixed end of the spring is at some position
x
o
. If a force acts at the unfixed end, its position will change to some new
value of x. The more force, the greater the departure of x from x
o
.
Chapter 5Analysis of Forces