Terminal speed and acceleration problem

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Discussion Overview

The discussion revolves around the acceleration of a ball thrown upwards at a speed greater than its terminal speed, considering the effects of air resistance and gravity. Participants explore the implications of terminal velocity and the forces acting on the ball during its motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that when the ball is thrown upwards at a speed greater than terminal speed, the acceleration may be less than, equal to, or greater than 9.81 m/s², depending on the forces acting on it.
  • One participant proposes that the acceleration due to air friction is equal to the gravitational force when the ball is at terminal speed, leading to a scenario where both forces act in the same direction when the ball is thrown upwards.
  • Another participant calculates that the minimum acceleration when thrown upwards is 19.62 m/s², based on the combined forces of gravity and air resistance, asserting that the acceleration is d) 19.62 m/s² or greater.
  • Some participants express uncertainty about whether more information is needed to determine the exact acceleration, suggesting that the answer could be option e) More information is required.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the acceleration of the ball when thrown upwards. Multiple competing views remain regarding the effects of air resistance and the conditions under which the acceleration can be determined.

Contextual Notes

There are unresolved assumptions regarding the conditions of the throw, the exact nature of air resistance at different speeds, and the definitions of terminal speed in this context.

MTBrider
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I'm having trouble figuring this one out. Hope someone can help

A ball dropped from rest accelerates at a rate of 9.81 m/s2 if we ignore air resistance. If air
resistance is not ignored, the ball reaches a terminal speed when the friction force of the air
acting on the falling ball is equal to the gravitational force acting upon the ball. If, instead of
being dropped, the ball is hurled upwards into the air at a speed greater than the terminal
speed the acceleration of the ball is…
a) 9.81 m/s2
b) less than 9.81 m/s2
c) greater than 9.81 m/s2 but less than 19.62 m/s2
d) 19.62 m/s2 or greater
e) More information is required.

I'm thinking you would need more information to actually pin down a number for the acceleration but I may be wrong. Would it be C, greater than g but less than 2g?
 
Last edited:
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At greater than terminal speed the acceleration due to air friction is (less/greater/equal) than g.

this acceleration is in the (same/opposite) direction as the acceleration due to gravity.

the sum of both is the acceleration you want.
 
Thank you, got it worked out
 
When the ball is falling downward at terminal speed the frictional air resistance is acting opposite to the direction of gravity, and the ball doesn't accelerate (since it's moving at constant velocity). Therefore, Friction = mg.

Air resistance/friction increases as speed increases. So if the ball is thrown up at a speed greater than the terminal speed, the force of air friction is at least equal to mg.

When the ball is thrown up, gravity and air resistance both act in the same direction (down).

Therefore, the minimum force acting on the ball is the force due to air resistance PLUS the force due to gravity, which is F = mg + mg = 2mg

Since F = ma, 2mg = ma, and a = 2g = 2*9.81 = 19.62 m/s^2 (minimum)

The acceleration of the ball is d) 19.62 m/s^2 or greater


MTBrider said:
I'm having trouble figuring this one out. Hope someone can help

A ball dropped from rest accelerates at a rate of 9.81 m/s2 if we ignore air resistance. If air
resistance is not ignored, the ball reaches a terminal speed when the friction force of the air
acting on the falling ball is equal to the gravitational force acting upon the ball. If, instead of
being dropped, the ball is hurled upwards into the air at a speed greater than the terminal
speed the acceleration of the ball is…
a) 9.81 m/s2
b) less than 9.81 m/s2
c) greater than 9.81 m/s2 but less than 19.62 m/s2
d) 19.62 m/s2 or greater
e) More information is required.

I'm thinking you would need more information to actually pin down a number for the acceleration but I may be wrong. Would it be C, greater than g but less than 2g?
 

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