The direction of
has already been determined to be in the direction opposite to
or at an angle of
south of west.
Significance
The numbers used in this example are reasonable for a moderately large barge. It is certainly difficult to obtain larger accelerations with tugboats, and small speeds are desirable to avoid running the barge into the docks. Drag is relatively small for a well-designed hull at low speeds, consistent with the answer to this example, where
is less than 1/600th of the weight of the ship.
In
Newton’s Laws of Motion , we discussed the
normal force , which is a contact force that acts normal to the surface so that an object does not have an acceleration perpendicular to the surface. The bathroom scale is an excellent example of a normal force acting on a body. It provides a quantitative reading of how much it must push upward to support the weight of an object. But can you predict what you would see on the dial of a bathroom scale if you stood on it during an
elevator ride? Will you see a value greater than your weight when the elevator starts up? What about when the elevator moves upward at a constant speed? Take a guess before reading the next example.
What does the bathroom scale read in an elevator?
[link] shows a 75.0-kg man (weight of about 165 lb.) standing on a bathroom scale in an elevator. Calculate the scale reading: (a) if the elevator accelerates upward at a rate of
and (b) if the elevator moves upward at a constant speed of 1 m/s.
(a) The various forces acting when a person stands on a bathroom scale in an elevator. The arrows are approximately correct for when the elevator is accelerating upward—broken arrows represent forces too large to be drawn to scale.
is the tension in the supporting cable,
is the weight of the person,
is the weight of the scale,
is the weight of the elevator,
is the force of the scale on the person,
is the force of the person on the scale,
is the force of the scale on the floor of the elevator, and
is the force of the floor upward on the scale. (b) The free-body diagram shows only the external forces acting
on the designated system of interest—the person—and is the diagram we use for the solution of the problem.
Strategy
If the scale at rest is accurate, its reading equals
, the magnitude of the force the person exerts downward on it.
[link] (a) shows the numerous forces acting on the elevator, scale, and person. It makes this one-dimensional problem look much more formidable than if the person is chosen to be the system of interest and a free-body diagram is drawn, as in
[link] (b). Analysis of the free-body diagram using Newton’s laws can produce answers to both
[link] (a) and (b) of this example, as well as some other questions that might arise. The only forces acting on the person are his weight
and the upward force of the scale
According to Newton’s third law,
and
are equal in magnitude and opposite in direction, so that we need to find
in order to find what the scale reads. We can do this, as usual, by applying Newton’s second law,
