# Does a truck's load affect its braking distance?

1. May 6, 2015

### mehgon

Two trucks with the same futures,one loaded and one empty. They are travelling on same speed and when they brake on the same spot;which one stops earlier? Does a truck's load affect it's braking distance?
Thanks..

2. May 6, 2015

### Staff: Mentor

Is this a homework problem?

What do you think the answer is?

3. May 6, 2015

### newjerseyrunner

The breaking distance has to do with how quickly it's velocity changes right? That's acceleration. The force that the breaks can apply does not change regardless of the size of the truck. The mass of the truck changes. force = mass * acceleration. So what happens to acceleration if force stays the same but mass increases?

4. May 6, 2015

### A.T.

The relevant force is the one that the road can apply.

5. May 6, 2015

### newjerseyrunner

Oh geez, that's right. Okay, the amount of force applied to the truck is the force of kinetic friction. The friction coefficient times the normal force.

6. May 6, 2015

### A.T.

If it slides, which the OP doesn't specify.

So assuming sliding with the same friction coefficient, and ignoring all other retarding forces, what is the answer?

7. May 6, 2015

8. May 8, 2015

### Lsos

As mentioned, in the real world the stopping distance IS affected by the load. This is a classic example of how a textbook and real life are not in agreement. Whether the stopping distance actually increases or decreases with more load depends on many factors. For example, the coefficient of friction might decrease which lengthens the stopping distance, but the truck might have been designed to perform better with a load, so the suspension/ tire position might result in better overall grip and a shorter stopping distance.

Other things keep this from being a good homework question. For example, a wider tire might give a better coefficient of friction...but is this true on all surfaces? Is it true in the snow/ rain?

9. May 8, 2015

### sophiecentaur

That's only true if the brakes are good enough to cause wheel slippage. Plenty of 'old' vehicles had the sort of brakes that would never cause a skid on a decent road surface. Under those conditions, the braking force could be considered independent of load (strength of the driver's right leg, in fact). But even if the limit is when the wheels slip, you can't treat the tyre / road friction as linear (not a constant coefficient of friction) so that makes good theory based predictions pretty difficult. With suitable choice of tyre and surface, I reckon you could get any answer you wanted to the OP.

10. May 8, 2015

### A.T.

It's always true. Only external forces can slow down the truck.

11. May 8, 2015

### sophiecentaur

Are you saying that the torque that is present in the brakes plays no part in the braking process? You can't be!
That torque is caused by the brake pad friction which is caused by pedal force ( in a passive system). If there is no skidding, then it is the brake torque that governs the rate of negative acceleration. It can be the dominating factor and is independent of load.

12. May 8, 2015

### jbriggs444

i.e. if the brakes are out, it doesn't matter how much force the road could otherwise provide.

13. May 8, 2015

### A.T.

Which isn't specified.

14. May 9, 2015

### sophiecentaur

I dealt with both eventualities. You could even assume ABS. I think you have to admit that the majority of times that vehicles stop does not involve skidding.
You can hardly ignore the action of the brakes within the vehicle in any discussion like this one.

15. May 9, 2015

### A.T.

My statement in post #4 also applies in both cases.

16. May 9, 2015

### sophiecentaur

That statement is actually wrong unless the wheels are slipping. In most circumstances the force is less than the limiting friction force between road and tyre. Can you possibly argue otherwise?

17. May 9, 2015

### A.T.

What is wrong about saying that only external forces can accelerate an object? That is true regardless of slipping or not.

18. May 9, 2015

### sophiecentaur

Nothing wrong with that. What is wrong is to associate that with the braking distance / mass relationship. The braking force is nearly always less than the limiting force on the tyres (which is proportional to the mass, where the simple basic law of friction applies). Mostly, the braking force is governed by the forces on the brake discs - which is independent of the mass. So the braking distance will be dependent on mass (surprise surprise).

19. May 9, 2015

### A.T.

I don't think questions like this want you to consider the infinite number of possible sub-optimal circumstances. The most reasonable way to compare the two braking situations is to assume optimal braking strategy in both cases, with the maximal ground friction possible in each case. Otherwise the answer becomes arbitrary.

20. May 10, 2015

### sophiecentaur

I realise you don't want to let this go but most trucks, when brought to a halt on most occasions, do not skid. (That's not one of any 'infinite' set of circumstances; it's the majority.) To my mind, it is not an unreasonable situation to consider. You mention "optimal braking strategy". Doesn't that imply non skidding? That implies that the wheels are not locked and that the braking force is a function of the brakes.
We both have to admit, of course, that we are ignoring the real complexities of the way tyres and roads interact. A heavy load could have a big effect on how the tyres cope with any surface water, for instance. That sort of stuff is way beyond a simple discussion. With no extra knowledge, we have to consider the linear situation where the coefficient of friction is independent of load (at least, I think so).