How does air resistance affect a ball's acceleration?

[Badgeray]

Homework Statement

A ball is thrown vertically upward with an initial speed of v0. It experiences a force of air resistance. The positive direction for all vector quantities is upward.

Does the magnitude of the acceleration of the ball increase, decrease, or remain the same as the ball moves upwards?

The Attempt at a Solution

The magnitude of the ball’s acceleration with air resistance increases as the ball moves upwards because air resistance acts downwards, and the acceleration due to gravity also acts downwards. Acceleration becomes more negative, increasing the magnitude of the acceleration.

For example, if the acceleration due to gravity is -9.80m/s2 and the acceleration due to air resistance is -1.00m/s2, then:

Acceleration without air resistance = -9.80m/s2
Acceleration with air resistance = -9.80m/s2 + (-1.00m/s2) = -10.8m/s2

Comparing only the magnitudes of the accelerations:

Magnitude of acceleration without air resistance = 9.80m/s2
Magnitude of acceleration with air resistance = 10.8m/s2

The magnitude of the acceleration with air resistance is greater than the magnitude of the acceleration without air resistance.

However, the AP exam (question 1a) has the same question and this is their answer:

Question: http://apcentral.collegeboard.com/apc/public/repository/_ap05_frq_physics_c_m_45648.pdf
Solution: http://apcentral.collegeboard.com/apc/public/repository/_ap05_sg_physics_c_me_46691.pdf

Since velocity is upward, air resistance is downward, in the same direction as gravity. The velocity will decrease, causing the force of air resistance to decrease. Therefore, the net force and thus the total acceleration both decrease.

Which answer is right? Did the AP solution maybe forget that the question asked for magnitude?

 

[haruspex]

You write that the acceleration will become more negative. Why so? What does drag depend on? Will drag increase as the ball rises?

 

[mfb]

That is a poor phrasing in the problem statement. You are not supposed to compare "acceleration with air resistance" with "acceleration without" (there your answer would be correct), the question asks for the time-evolution of the accelerating while the ball is moving upwards.

 

[Mister T]

Magnitude of acceleration without air resistance = 9.80m/s2
Magnitude of acceleration with air resistance = 10.8m/s2

The magnitude of the acceleration with air resistance is greater than the magnitude of the acceleration without air resistance.

As mfb points out, that is not the comparison they're asking you to make. As the ball continues its upward movement, will the magnitude of the acceleration stay at 10.8 m/s², will it decrease, or will it increase?

(I don't see poor phrasing, though).

 

[Badgeray]

That is a poor phrasing in the problem statement. You are not supposed to compare "acceleration with air resistance" with "acceleration without" (there your answer would be correct), the question asks for the time-evolution of the accelerating while the ball is moving upwards.

Thanks, I understand now. What about the downward part of the ball's path? Would acceleration increase?

 

[Mister T]

Thanks, I understand now. What about the downward part of the ball's path? Would acceleration increase?

At the highest point in the trajectory the speed is zero so the acceleration has a magnitude of g. After that, what happens as the speed increases? Hint, eventually a terminal velocity is reached and the acceleration is zero.

 

[mfb]

(I don't see poor phrasing, though).

As you can see, it is possible to misinterpret the question. Some additional "over time" would have made it much clearer.

Thanks, I understand now. What about the downward part of the ball's path? Would acceleration increase?

What do you expect?

 

[Badgeray]

At the highest point in the trajectory the speed is zero so the acceleration has a magnitude of g. After that, what happens as the speed increases? Hint, eventually a terminal velocity is reached and the acceleration is zero.

Ah, so the acceleration decreases until it reaches its terminal velocity.

 

[mfb]

Its magnitude decreases, right.