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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 --->

       ------------            ------------
                  |            |
                  |            |
                  |            |

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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