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Weight and Car Crossing a Cliff
Name: Kiran
Status: other
Age: 20s
Location: N/A
Country: N/A
Date: 2000-2001
Question:
Hi,
I really appreciate the quick response.
I have another question.
Let us say there is no plank at all between the
two supports.
CAR --->
------------ ------------
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The car at high speed (Less than light speed of course)
lets say 120 MPH ,would still cross the cliff (say a
distance of 10 Meter)without falling.
So whether there is plank or not,The car does not seem to
put weight at all during that period.(And also the effect
of Air is not so much as to believe that it is flying).
(I guess Kinetic energy is responsible here,But was curious
to know more in detail)
What makes the car to cross the cliff without falling?
And also as the speed of the car is increased the distance
it crosses without falling also increases.
Or in other words,Even when the car is moving with such a speed on
ground,The weight on the ground should be lesser?
Replies:
Sorry, the car will fall when nothing (such as the ground or a bridge) holds
it up. Now, if it had been moving slightly upward when it left the ground,
it would still at least initially continue moving upward, but all the same
it would accelerate, due to gravity, downward. The only way this could be
avoided is if the car had an airfoil shape, so that the air pushes up on it.
It SEEMS as though the car does not fall because in the short period of time
that the car hurdles over the gap it doesn't have time to fall very far.
Let's say that the car in your example, traveling at 120 miles per hour,
traverses a 10 meter gap. (Your mixing of units makes the computation more
of a pain than it should be.) 120 miles per hour = 53.6 meters per second,
so the car will be unsupported for about one fifth of a second. In that
time, the car will drop about 7 inches (further mixing units). Unless the
car had really big tires, it would probably be in trouble when it reached
the far edge of the chasm.
Now, if the chasm were only ten feet wide, the car would drop less than an
inch before reaching the far side, which would be equivalent to just a small
bump in the road. No problem at all.
Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
The second the car's front wheels cross over into the unsupported
space, the front of the car begins to fall at an acceleration of 9.8
m/s/s. Suppose it takes t seconds for the wheels to arrive at the end
of the unsupported space. After t seconds, the front wheels will have
fallen (9.8/2)*t^2 meters. If this distance is much less than the
radius of the front wheel, the car will continue on with only a little
bump.
Tim Mooney
Actually, the car does fall. However, the distance the car falls downward
is limited by the length of time the car is in the air. Assume the car
takes off in a perfectly horizontal direction. It will drop a distance of
approximately (1/2)gt^2, where t is the time required for the car to reach
the far side of the cliff. Let us assume the car is traveling at 100m/s.
The "time-of-flight" will be only 0.1 seconds. The car will have dropped a
distance of approximately (5 m/s^2)*(0.1 s)^2, or 0.05 m = 5 cm. A distance
of 5 cm is a distance of 2 inches. The wheels will have no trouble
"catching" the edge of the cliff: the car will not fall.
Kenneth Mellendorf
At high speeds the time to cross the gap is less. It's not that the car
doesn't fall but rather that it doesn't fall enough to prevent it from
continuing over the lip of the gap on the other side.
If you performed the experiment with a car to see how wide a gap it could
jump at different speeds you would find that the time the car spends over
the gap (falling) is constant. Any more time (wider gap) and the car has
fallen too far to make it over the lip of the gap on the other side.
This does not really involve kinetic energy, but acceleration due to
unequal forces. The acceleration is equal to the unbalanced force divided
by the mass. Since the mass of the car is constant we can focus on what is
happening with the forces.
In you experiment you are changing, suddenly, the force pushing up from the
car. When the car is on the ground the force pushing up is exactly equal
to the weight of the car and the car does not sink into the earth. When the
car passes over the edge of the gap the upward force is suddenly removed
and the car responds to the unbalanced force by starting to move downward.
It doesn't suddenly jump to the bottom of the gap but smoothly accelerates
toward the bottom at 9.8 m/(s^2) -- the acceleration due to gravity on
earth. If a planck is present, the same thing occurs except now there is
some force pushing up on the car and it will accelerate less quickly and
the board will flex as the car falls. When the board flexes too far it
will break and the car will again accelerate at 9.8 m/(s^2).
Greg Bradburn
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Update: June 2012
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