Stopping in min. distance[friction]

[vissh]

Homework Statement

(Q)In order to stop a car in shortest distance on a horizontal road, one should :-
<a>apply the brakes very hard so that the wheels stop rotating
<b>apply the brakes hard enough to just prevent slipping
<c>pump the brakes
<d>shut the engine off and not apply brakes

Homework Equations

When a body slips on a surface & the body and surface are rough,the kinetic friction start to act.

The Attempt at a Solution

I think <a> is correct as if the wheels start to slip the kinetic friction will act on car which is > or = to frictional force in other cases and also in <a> this friction will act continuosly.
But the answer in book is <b> oO. [I think in <b> ,rolling friction will act which is less than kinetic friction]
Can anyone guide me :)
Thanks in advance ^.^

 

[PhanthomJay]

Well, there's a little bit of rolling friction in there, usually very small and much less than the kinetic friction force. Predominantly, the friction force slowing down the car is the static friction force, which is greater than the kinetic force while sliding, and which occurs as long as the wheels are still rotating, maximized just before slipping occurs.

 

[tiny-tim]

hi vissh!

I think <a> is correct as if the wheels start to slip the kinetic friction will act on car which is > or = to frictional force in other cases and also in <a> this friction will act continuosly.
But the answer in book is <b> oO. [I think in <b> ,rolling friction will act which is less than kinetic friction]

no, it's best not to talk about rolling https://www.physicsforums.com/library.php?do=view_item&itemid=39" …

there are two types of friction: kinetic and static …

when a wheel slides, that's kinetic friction; when a wheel rolls, that's static friction …

in both cases there is also a very small loss of energy (due mostly to deformation of the wheel and tyre), which it is better to call rolling resistance

(b) was correct because static friction is larger than kinetic friction

 

[vissh]

Thanks both of you ^.^
Got a thing to ask :- When the brakes are applied and the wheel just rolls on road[no slipping], does this "braking" gives the point of contact a tendency to move in direction of original motion Due to which the static friction acts on the opposite direction of motion [And thus,the body slows down]? oO

 

[tiny-tim]

hi vissh!

sort of …

the whole friction-on-rolling-wheels thing is rather perplexing …

when a car is accelerating, the friction on the driving wheels (from the road) is forward, but the friction on the other wheels (from the road) is backward!

and yes, on braking, the friction force on the braked wheels (from the road) is backward, causing the car to decelerate

this is caused by a friction force from (essentially) the chassis on the wheels, slowing the rotation, and causing the wheels to exert a friction force forward on the road: the equal backward reaction force from the road on the wheels decelerates the car

to find the direction of friction, always ask "what would happen if there was no friction?" (for example, if one surface was ice) …

if the car is braking (on ice), the braked tyre will go slower, but the car will stay the same speed (because there are no forces on it): looking down from the window, you see the road going backward faster than the tyre is going backward, so the road is going faster backward than the tyre, and it will try to drag the tyre with it

in other words: the tendency is for the road to move backward relative to the tyre, so the friction on the road is forward, and the friction on the tyre is backward

however, the non-braked tyres (usually the front, steering, tyres) will have a forward friction force from the road at the same time …

if the car is braking, and if the non-braked tyres only are on ice, the non-braked tyre will go at the same speed, but the car will go slower: looking down from the window, you see the road going backward slower than the tyre is going backward, so the road is going slower backward than the tyre, and it will try to drag the tyre with it

in other words: the tendency is for the road to move forward relative to the tyre, so the friction on the road is backward, and the friction on the tyre is forward

this of course is why 4-wheel braking slows a car faster than 2-wheel!​

by comparison:
if the car is accelerating (on ice), the non-driving tyre will stay the same speed (because there are no forces on it), but the car will go faster: looking down from the back window, you see the road going backward faster than the tyre is going backward, so the road is going faster backward than the tyre, so it will try to drag the tyre with it

in other words: the tendency is for the road to move backward relative to the tyre, so the friction on the road is forward, and the friction on the tyre is backward

But if the car is accelerating (on ice), the driving tyre will go faster (because the engine is puling it … the lack of friction doesn't matter), but the car will stay the same speed (because there are no forces on it): looking down from the back window, you see the road going backward slower than the tyre is going backward, so the road is going faster forward than the tyre, so it will try to drag the tyre with it

in other words: the tendency is for the road to move forward relative to the tyre, so the friction on the road is backward, and the friction on the tyre is forward!

 

[vissh]

Thanks Thanks a lot tim :D
Really appreciate your help ^.^