"Elevator Up!"
Biomechanics Lab
Newton's Laws
Julieanne Abendroth-Smith
University of Utah
Learning Objective: To increase understanding of
Newton's Laws of Motion and it's applications.
Equipment:
bathroom scale
elevator
Background:
What does a bathroom scale show when you stand on it?
Does it always indicate your weight? Can you get it to show a value greater
or lesser than your weight for an instant?
A bathroom scale is actually a force measuring device.
It indicates the size of the normal reaction force which acts between your
feet and the floor (or top of the scale).
The figure to the right shows a free body diagram of someone
standing on a bathroom scale. |
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Newton's Second Law gives this equation:
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? Fy
= may
|
where ? Fy
= net vertical force
m = mass
ay = vertical
acceleration |
If upward is considered to be positive, then the equation
of
motion for the person on the scale becomes
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? Fy
= R-W = may
|
where R = the reaction force from
the scale
W= the weight of the person on the scale
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If the person's weight is known, then the scale reading
can be used to determine the direction of the acceleration as follows:
IF THEN AND
R > W net force is positive (upward) acceleration is positive
(upward)
R = W net force is zero acceleration is zero
R < W net force is negative (downward) acceleration
is negative (downward)
Activities and Questions:
1. Newton's First and Third Law while standing on a scale
While standing still on the scale, push as hard as you
can against the scale and determine the maximum reading that you can maintain
on the scale, i.e. how hard can you push against the scale for two seconds
if you don't move or touch anything else other than the scale.
Can you push against the scale with a force greater than
your weight? If not, why not? How big is the force that the scale pushes
back against you?
2. Newton's Second law while squatting on the scale
Stand still with your hands on your hips. Note your
weight. Lower yourself to a squatting position. Observe what happens to
the scale reading as you squatted. Stand back up and observe the scale
readings as you stand up.
Complete the following table by indicating whether the scale
reading was less than, equal to, or greater than your weight and indicate
the direction of your corresponding accelerations while you squatted and
stood up.
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Is the scale reading(R) less than (<), equal to
(=) or greater than(>) your weight (W)?
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Acceleration Direction
(down, zero, up)
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SQUATTING
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starting down |
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DOWN
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slowing |
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stopped |
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STANDING
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starting up |
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UP
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slowing |
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stopped |
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What is the relationship between the scale reading and
your acceleration? Experiment further by lifting your arms up or by lifting
and lowering some objects to see if this relationship holds for other movements
as well.
3. Newton's Second Law while riding an elevator
Stand still in an elevator as it goes up, stops, goes
down, and stops. Observe what happens to the scale reading as the elevator
starts up, continues up, slows down, stop, starts, down, continues down,
and stops.
Complete the following table by indicating whether the scale
reading was less than, equal to, or greater than your weight and indicate
the direction of your corresponding accelerations while you rode the elevator.
| |
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Is the scale reading(R) less than (<), equal to
(=) or greater than(>) your weight (W)?
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Acceleration Direction
(down, zero, up)
|
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ELEVATOR
|
starting up |
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MOVING
|
continuing up |
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UP
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slowing down |
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|
| |
stopped |
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|
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ELEVATOR
|
starting down |
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MOVING
|
continue down |
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DOWN
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slowing up |
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|
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stopped |
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Does the relationship between the scale reading and
your acceleration still hold true for the elevator? Was there any time
during the elevator ride when you were moving downward but the net force
acting on you was zero? When do you feel "heavier" during the elevator
ride? Why? When do you feel "lighter" during an elevator ride? Why? How
do you sense your weight?
4. Acceleration of the elevator
Stand still on the scale in the elevator. Note your
weight. Record the scale reading as the elevator moves up and down. The
change in your weight is the net force acting on you, causing your body
to accelerate, decelerate or remain at a constant velocity.
Complete the following table to calculate the accelerations
of you ( and the elevator) at the various stages of motion.
Weight (W)_________Lbs Mass (weight / 32 ft/s/s) _________slugs
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Reaction force (R)
(Scale reading)
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Fnet = R- W
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acceleration
a = Fnet / mass
(ft/s/s)
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ELEVATOR
|
starting up |
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MOVING
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continuing up |
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UP
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slowing down |
|
|
|
| |
stopped |
|
|
|
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ELEVATOR
|
starting down |
|
|
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MOVING
|
continue down |
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|
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DOWN
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slowing up |
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stopped |
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Are the accelerations of the elevator the same for both
directions? If not, what would account for the differences? What does an
acceleration equal to zero mean?