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

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SUMMARY

The discussion centers around the differences in acceleration between a bowling ball and a football when accounting for forces such as gravity and air resistance. The bowling ball, with a weight of 10 N and an effective force of 9.95 N, results in an acceleration of 9.95 N/kg. In contrast, the football, with a mass of 0.5 kg and an effective force of 4.95 N, yields an acceleration of 9.9 N/kg. The discrepancy arises from the differing weights and the impact of air resistance on each object, leading to the conclusion that their accelerations are not equal due to these factors.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Basic knowledge of gravitational force (W = mg)
  • Familiarity with the concept of air resistance
  • Ability to perform calculations involving forces and mass
NEXT STEPS
  • Research the effects of air resistance on different shapes and masses
  • Study the principles of projectile motion in physics
  • Explore advanced topics in dynamics, such as drag coefficients
  • Learn about the implications of mass and weight in real-world applications
USEFUL FOR

This discussion is beneficial for physics students, educators preparing GCSE materials, and anyone interested in the practical applications of Newtonian mechanics in sports and motion analysis.

polekitten
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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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