Why are the accelerations of the bowling ball and football not equal?

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The discussion centers on the misconception that a bowling ball and a football should have equal accelerations when dropped, despite differing weights and air resistance. The bowling ball experiences a net force of 9.95 N, resulting in an acceleration of 9.95 N/kg, while the football has an effective force of 4.95 N, leading to an acceleration of 9.9 N/kg. The key point is that air resistance affects the football more significantly due to its lower mass, resulting in different accelerations. The original question reflects confusion about the impact of air resistance on falling objects. Understanding these forces clarifies why their accelerations are not equal.
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1. What have I done wrong when I set this GCSE question?! (shortened)
Gravity: 10 N/kg
Bowling ball: weight 10 N, air resistance 0.05 N, overall force 9.95 N
Football: mass 0.5 kg, air resistance 0.05 N

Students need to work out:
  • effective force on the football (4.95 N)
  • bowling ball (a = F/m = 9.95 / 1 = 9.95 N/kg)
  • football (a = F/m = 4.95 / 0.5 = 9.9 N/kg)
So... what have I messed up as I'm pretty sure their acceleration should be equal!?

Homework Equations


F = ma, W = mg

The Attempt at a Solution


I have played around with it and I'm missing something, help!
 
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polekitten said:
So... what have I messed up as I'm pretty sure their acceleration should be equal!?
Why should the acceleration be the same when you take into account air resistance?
 
Dumb... thanks for pointing out the obvious!
 
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