A regular tennis ball and another one filled with sand are dropped at the same time from the top of a high building. Your friend says that even though air resistance is present, both balls should hit the ground at the same time because they are the same size and "plow through" the same amount of air. What do you say?
2006-12-15 08:46:34 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Physics
I like what Raymond has to say, and I'll add just a bit to clarify. Newton's second law, as you alluded to, says that the sum of the forces acting on an object is equal to the product of the object's mass and total acceleration. In this case, the forces acting on each ball (to borrow Raymond's notation):
F(e) = cv(e)^2 + m(e)g
F(f) = cv(f)^2 + m(f)g.
The term cv^2 is the quadratic drag force acting on each of the tennis balls. There is also a linear term, but the quadratic dominates the expression. Anyway, those forces are also equal to
F(e) = m(e) a(e)
F(f) = m(f) a(f).
Set these sets of equations equal to each other, and you will find that the final acceleration on each is
a(e) = cv(e)^2/m(e) + g
a(f) = cv(f)^2/m(f) + g.
Since m(f) > m(e), a(e) > a(f), and thus the full ball will accelerate more.
2006-12-15 09:44:11 · answer #1 · answered by woocowgomu 3 · 0⤊ 0⤋
If you make the assumption that there is no air resistance acting on the balls, both will hit the ground at the same time as gravity accelerates all objects at the same rate regardless of mass. However, if you take air resistance into account and your building is sufficiently tall so air resistance has an effect on the balls, the more massive one will hit the ground first as it has a larger terminal velocity due to its higher weight (force caused by gravity).
2006-12-15 16:53:26 · answer #2 · answered by msi_cord 7 · 3⤊ 0⤋
At the same speed, the force from air resistance (F) will be the same on both balls.
However, the acceleration that will reduce the speed of fall will be less on the more massive ball than on the other.
F = m a
Empty ball: F = m(e) * a
a(e) = F / m(e)
Full ball: F = m(f) * a
a(f) = F / m(f)
Since F is the same in both cases and since m(e) is less than m(f), then it follows that a(e) is greater than a(f).
Air resistance is a force opposite the direction of movement. Both balls are falling thus F points upwards and a will reduce the speed.
Therefore the full ball will gain on the empty ball.
2006-12-15 17:27:37 · answer #3 · answered by Raymond 7 · 0⤊ 0⤋
False, the one with sand has more mass.
If we have the same resistance and surface area, the ball with more mass will have more weight because more mass is being pulled down by the force of gravity.
However, if we have it dropped in a vacuum, then they would fall down at the same time.
2006-12-15 16:51:28 · answer #4 · answered by Bao L 3 · 0⤊ 2⤋
My friend is correct. The velocity will be determined by the size, shape, and aerodynamic resistance of the balls, not their mass.
2006-12-15 17:18:49 · answer #5 · answered by rb42redsuns 6 · 0⤊ 0⤋
Correct, because mass has nothing to do with the acceleration due to gravity.
2006-12-15 16:49:17 · answer #6 · answered by dgbaley27 3 · 0⤊ 0⤋