Will a Ball Take Longer To Rise or Fall?

In summary, the question is whether it would take longer for a ball to drop back to its original position from its max height or longer for the ball to rise up to its max height, taking into account air friction. The conclusion is that on the way down, there is only one resistive force (air friction), so the ball would fall faster. However, air friction decreases the acceleration in this problem. The net force on the way up is -(F_g + F_a), and on the way down it is -F_g + F_a, resulting in the same amount of time for the ball to go up and down.
  • #1
UrbanXrisis
1,196
1
if I threw a ball straight up (including air friction), would it take longer for the ball to drop back to its original position from its max height or longer for the ball to rise up to its max height?

here's what I'm thinking, on the way up, there is air friction and mg going agaist the initial velocity, on the way down, it would just be air friction against the ball. Since on the way down, there is only one resistive force, then it would fall faster right?

also, air friction in this problem decreases the acceleration right?
 
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  • #2
here's what I'm thinking, on the way up, there is air friction and mg going agaist the initial velocity, on the way down, it would just be air friction against the ball. Since on the way down, there is only one resistive force, then it would fall faster right?

So mg doesn't act on the way down? Are you sure?
 
  • #3
the resistive force on the way up would be F=Fg+Ff

on the way down it would be F=Ff

since there is less resistive force on the way down, the ball would drop faster
 
  • #4
Net force on the way up, with up as positive:

[tex] -(F_g + F_a) [/tex]

Down:

[tex] -F_g + F_a [/tex]

Finding:

[tex] -F_g - F_a (?) -F_g + F_a [/tex]

Cancel -F_g

[tex] -F_a (?) F_a [/tex]

F_a is acting AGAINST the direction of motion in both directions. It's still my opinion that it takes the same time to go up and down.
 

Related to Will a Ball Take Longer To Rise or Fall?

1. Will a ball take longer to rise or fall?

The time it takes for a ball to rise or fall depends on the initial conditions of the ball, such as its mass, shape, and initial velocity. In a vacuum, a ball will take the same amount of time to rise and fall. However, in the presence of air resistance, a ball will take longer to fall due to the drag force acting on it.

2. How does air resistance affect the time it takes for a ball to rise or fall?

Air resistance, also known as drag force, is a force that opposes the motion of an object through the air. This force increases as the speed of the object increases. Therefore, in the presence of air resistance, a ball will take longer to fall due to the drag force acting on it. On the other hand, air resistance will not affect the time it takes for a ball to rise.

3. Does the mass of the ball affect the time it takes to rise or fall?

Yes, the mass of the ball does affect the time it takes to rise or fall. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, a heavier ball will take longer to fall compared to a lighter ball, assuming all other factors are the same.

4. Why does a ball take longer to fall than to rise?

A ball takes longer to fall than to rise due to the presence of air resistance. When a ball is thrown up in the air, it has an initial upward velocity that helps it overcome the force of gravity and rise. However, when it is falling, the force of gravity is acting in the opposite direction, and the air resistance acts to slow down the ball, causing it to take longer to fall.

5. Can the shape of the ball affect the time it takes to rise or fall?

Yes, the shape of the ball can affect the time it takes to rise or fall. A more streamlined shape will experience less air resistance compared to a more irregular shape. Therefore, a ball with a more streamlined shape will take less time to fall compared to a ball with a more irregular shape, assuming all other factors are the same.

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