Can a heavier car reach higher top speed rolling down a steep?

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Discussion Overview

The discussion revolves around whether a heavier car can achieve a higher top speed when rolling down a steep slope compared to a lighter car. Participants explore the effects of weight on acceleration, speed, and various forces acting on the cars, including gravity, rolling resistance, and air resistance.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that the heavier car will accelerate slightly faster due to the proportionality of gravitational and rolling resistance forces to weight.
  • It is proposed that because of this increased acceleration, the heavier car will also reach a higher speed and have a higher terminal speed when gravity equals air resistance.
  • Others argue that the outcome depends on various factors, including the angle of the slope, the quality of bearings, tire characteristics, and road conditions, which may influence the overall dynamics.
  • A later reply introduces the concept that increased mass could lead to higher rolling resistance and bearing friction, potentially affecting the terminal velocity in a complex manner.

Areas of Agreement / Disagreement

Participants express differing views on the impact of weight on speed, with some asserting that a heavier car will go faster while others highlight the influence of additional factors, indicating that the discussion remains unresolved.

Contextual Notes

Limitations include the dependence on specific conditions such as slope angle and road quality, as well as the unresolved relationship between mass and rolling resistance in the context of terminal velocity.

karabiner98k
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Hi everybody,
The question is that we have two cars with similar specifications except that one of them is heavier than the other.
I was told that the heavier car can go faster on a steep because of more weight.
Is that true?
 
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welcome to pf!

hi karabiner98k! welcome to pf! :smile:

the force of gravity, and the force of rolling resistance (and i think also the friction in the bearings), are both proportional to weight (or mass)

but the force of air resistance is proportional to surface area

so two identical cars rolling downhill with the engine off, one heavily laden, will feel the same air resistance, but the other forces will be proportional to weight, so yes, the heavier car will accelerate slightly faster :wink:
 


tiny-tim said:
hi karabiner98k! welcome to pf! :smile:

the force of gravity, and the force of rolling resistance (and i think also the friction in the bearings), are both proportional to weight (or mass)

but the force of air resistance is proportional to surface area

so two identical cars rolling downhill with the engine off, one heavily laden, will feel the same air resistance, but the other forces will be proportional to weight, so yes, the heavier car will accelerate slightly faster :wink:
Thanks for your answer.
What about the speed? Can the heavier car reach a higher speed than the lighter one?
 
Since its acceleration is always slightly more, its speed will be also.

And its terminal speed (when gravity equals air resistance) will be slightly higher too, for the same reason. :smile:
 
Huh, it depends on the angle of the slope, the quality of the bearings, the pressure, size, and quality of the tires, and the quality (roughness) of the road.

Check terminal velocity Vt =...):
http://en.wikipedia.org/wiki/Terminal_velocity

But if you include all forms of friction in Cd above, (not just air drag), Cd becomes a function of mass m i.e. increased mass means increased rolling resistance (tire and road dependent) and bearing friction. Both increase Cd, which may in turn decreases Vt. It will depend on the ratio m/Cd(m). The effect of the mass on Cd(m) will depend on the angle of the slope.
 
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