- #1

jaumzaum

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- Homework Statement
- When designing a highway and its signaling system, it is necessary to consider variables that can interfere with the minimum distance required for a vehicle to stop. Consider a situation in which a car travels at a constant speed along a flat, horizontal road, with a fixed coefficient of static and dynamic friction and that, in a certain point, starts to brake, decelerating uniformly until it stops, without slipping. Disregard losses due to air resistance and friction between the mechanical components of the vehicle. Regarding the minimum braking distance, in the situations described, the following statements are made:

a) It increases proportionally to the car's mass.

b) It is inversely proportional to the coefficient of static friction.

c) It is not related to the acceleration of local gravity.

d) It is directly proportional to the square of the car's initial speed.

- Relevant Equations
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I'm a little confused about this question because I think the braking deceleration probably takes into account the braking system of the vehicle as well as the power of the motor. I don't understand how a car could actually brake without the "friction between the mechanical components of the vehicle". I don't understand how braking systems works, but I think it has something to do with trying to decelerate the wheels axle, and that can only be done by friction in my opinion.

Also, consider the following situation: a wheel is moving in a horizontal plane without slipping. In a stationary situation, where the v=wr, there v is the center of mass velocity, there is no friction being applied in the wheel, and it will move with a constant angular velocity and a constant center of mass velocity according to first Newton law.

If friction were applied to that wheel in a condition of no slipping, it would have to be static friction. But for friction to be applied, it would also need to exist another external force or torque (i.e. from the mechanical parts), as discussed above. With no external force or torque, there could be no friction.

So, judging the alternatives, I would say a) is a little confusing, because if we keep the "braking power" constant (the maximum force or torque that the braking system can apply in the wheels), and we increase the car mass, we would be reducing the deceleration, as well as increasing the distance.

b) makes sense, but only if we consider only friction going on.

c) also makes sense, also if we only consider friction going on.

d) the only that I would say is always correct, by Torrichelli.

Also, consider the following situation: a wheel is moving in a horizontal plane without slipping. In a stationary situation, where the v=wr, there v is the center of mass velocity, there is no friction being applied in the wheel, and it will move with a constant angular velocity and a constant center of mass velocity according to first Newton law.

If friction were applied to that wheel in a condition of no slipping, it would have to be static friction. But for friction to be applied, it would also need to exist another external force or torque (i.e. from the mechanical parts), as discussed above. With no external force or torque, there could be no friction.

So, judging the alternatives, I would say a) is a little confusing, because if we keep the "braking power" constant (the maximum force or torque that the braking system can apply in the wheels), and we increase the car mass, we would be reducing the deceleration, as well as increasing the distance.

b) makes sense, but only if we consider only friction going on.

c) also makes sense, also if we only consider friction going on.

d) the only that I would say is always correct, by Torrichelli.