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Name: D. F.
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 2000-2001


Question:
a .060kg tennis ball and a 4.55kg bowling ball sitting on a ladder at 3.1m above the ground they fall off simutaneously which will hit the ground first and why?


Replies:
Assuming that they are falling in air and not in a vacuum, the bowling ball will almost certainly hit the ground first. The reason is that their acceleration toward the ground is determined by the forces acting on them divided by their masses. The force due to gravity is exactly proportionate to their masses, so if that were the only force acting on them, both balls would fall at exactly the same rate. However, gravity isn't the only force.

Once the balls are moving through the air, they experience a force from wind resistance as well. This force will oppose the downward motions of the balls. The overall acceleration of each ball will be governed by the sum of the forces from gravity and wind resistance, divided by the mass of the ball.

The force acting on a ball from wind resistance depends on its airspeed, its shapes, and its size. Because the bowling ball is bigger than the tennis ball, it will experience more force from wind resistance. However, when this force is added to the gravitational force (since these forces act in opposite directions, you could also say that you're subtracting the force of wind resistance from the gravitational force), it will change the total force acting on the bowling ball by only a small fraction. However, when you do the same subtraction for the tennis ball, the wind resistance will be a larger fraction of the total force. In other words, wind resistance will interfere with the tennis ball's fall more than with the bowning ball's drop. So, the bowling ball lands first.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois


According to Newton's law of gravitation, neglecting the resistance of air, both will hit the ground at the same time. Newton's law of gravitation states that the acceleration due to gravity is a constant, call it "g". This acceleration is a constant regardless of the mass of the object. This means that the speed that the falling objects, call it "s", is the acceleration "times" the time of fall, that is: s = g*t. That is the speed increases linearly with time with a slope of "g". This, in turn, means that the position of the object, call it "x", at some time "t" is: x = 1/2*(g*t^2). These formulas are derived from Calculus.

Without worrying about the mathematics, the important point is that the position of the falling objects depends only on "g" which is a constant, and the duration of fall "t". The mass of the object does not enter into equation.

Note that this is a "law" that is a statement of observations. It does not depend upon any "theory" about "how" or "why". It only states the results of many observations.

Vince Calder


Mr. Fluke,

This can be done without mathematics. First, look at the problem in a vacuum: no air. Both balls feel exactly the same acceleration. Both start at exactly the same velocity (zero). Their motions will be identical. They will reach the ground at exactly the same time.

Now, include the air. As they begin to speed up, air resistance will affect the motion of the tennis ball much more than that of the bowling ball. To verify this, place a bowling ball and tennis ball on a table. Blow on both as hard as you can. You can get the tennis ball moving. You have no effect on the bowling ball. Both balls are slowed, but the tennis ball is slowed more. The tennis ball will therefore take more time than the bowling ball to reach the ground. The greater the height of the ladder, the more noticeable the effect will be.

Dr. Ken Mellendorf
Illinois Central College



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