I’m once again teaching a First Year Seminar class at UC Davis on High Performance Driving. I just gave them a homework problem, so I thought I bring some of that here too. The lesson was about grip, so let’s start with the laws of friction.
Laws of Friction
- Amontons’ First Law: The force of friction is directly proportional to the applied load.
- Amontons’ Second Law: The force of friction is independent of the apparent area of contact.
- Coulomb’s Law of Friction: Kinetic friction is independent of the sliding velocity.
Questions
- Two identical cars are traveling 60 mph. Car A has just the driver. Car B has 3 additional passengers. Which car stops first?
- Two identical cars are traveling 60 mph. Car A has 195 width tires. Car B has 205 width tires. Which car stops first?
- Two identical cars are slowing down from speed by stomping on their brakes. Car A is going 60 mph. Car B is going 100 mph. Which driver feels more G-force?
- Why do racecars have slick tires?
you suck at racing 
1)
KE_a=0.5(m_a)(60^2); KE_b=0.5(m_b)(60^2)=0.5(m_a+X)(60^2)
f_a=μ(m_a)g; f_b=μ(m_b)g=μ(m_a+x)g
KE_a=f_a*s_a; KE_b=f_b*s_b
s_a=0.5(m_a)(60^2)/μ(m_a)g; s_b=0.5(m_a+X)(60^2)/μ(m_a+X)g
s_a=0.5(60^2)/μg; s_b=0.5(60^2)/μg
∴ s_a=s_b
2) No math to show, no area component in frictional force eqn. to cancel. Stop the same.
3) No math to show, no velocity component in frictional force eqn. to cancel. G force the same.
4) Because racecar.
Alternatively, coefficient of friction is a variable not a constant, and rubber is weird.
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A++
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To answer question #3 we need to know about the aero on the car. Drag and downforce will both increase braking gees at 100 mph vs 60, lift will decrease them.
There’s also a minor amount more drag on the car with 205 tires in question #2 as well.
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Yeah, the point of the question is that it’s a lot more complex than the Laws of Friction
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Sounds like fun. One of my favorites: “You’re driving in a racecar with no brakes towards a u-turn at 100mph (doesn’t really matter) when the engine shuts off. Coasting in neutral you manage to safely navigate the turn and are now moving in the opposite direction – again, without using the engine or the brakes. How?” Its one of those fun ones that seems super obvious until you try to explain it to someone.
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Ok, totally random question. I have a chance to get a Spec Racer Ford for not too much. Thoughts? Currently running a 1969 bmw 2002 that sorta needs some upgrades for track days… slow, surprisingly fun, and so far cheap.
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I’ve wanted one a “real race car” for a long time. That could be a Spec Racer Ford, Thunder Roadster, FF, FV, etc.
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