Physics, Chemistry, Mathematics Forums

It is a multiple choice question its ans is (a) & (b)

According to me the answer should be b) because in this case limiting friction will act while in case a) kinetic friction.Since static friction > kinetic friction
the body will be stopped in a lesser distance
What's the correct answer?

I think we can think in this way:-Wheels of car perform rolling motion.Friction cannot do any work ,for sure,in case of rolling motion but can apply torque if point of rotation is taken the centre of the wheel.If we apply brakes hard enough to stop the wheels from rotating then wheels may slip and if they slip kinetic friction will act.Since the wheels are decelerating and friction does not like relative motion,friction is going to act opposite to the direction of displacement.So,the work done by friction will be negative and wheels will travel less distance.If we prevent the wheels to slip,then any friction whether it is kinetic or static is not going to do any work and hence the distance travelled is more.In pump and release,slipping may occur for a very short time so distance travelled may be less but not less than the case of option (b). Please comment on this whether it seems to be correct or not.

To stop the wheel one needs to decease the v_cm of the wheel. For pure rolling, \(v_{cm}=r\omega\). If \(\omega\) decreases, v_cm also decreases. When brake is applied, \(\omega\) decreases and hence v_cm decreases as long as pure rolling is taking place. However, while driving one cannot afford to make \(\omega\) zero by applying very hard brakes as this causes sliding and the vehicle may go out of control (steering won't work properly for example during skidding besides other issues). So, one would want to decrease \(\omega\) to maximum extent without getting into the trouble caused by skidding.

PS: While Physics may point at option (b) theoretically, while actually driving car it is difficult to know precisely if you are pressing the brakes hard enough (i.e. not too hard, not too soft) and you may end up pressing and releasing & so on... to get what you intend doing.