How can you find out the braking force in newtons of a vehicle's braking system?

Question

I've been handed a physics problem and I need to find some resource to either convert or locate the force applied by a vehicles (large automotive) brakes.

Answer 1

One way to get an estimate is to do a test where you apply the brakes to the moving car, and measure the time required to reduce the speed by some amount (you could go all the way to a stop but that would probably exaggerate the error inherant in this estimate).

If you were going 100 km/hr , and you applied the breaks and dropped to 25 km/hr in 3 seconds, and you assumed a constant braking force, you could calculate that force (given the weight of the car, and ignoring air resistance and miscellaneous frictional decellerators)

First you calcualate the deceleration "a" needed to change the speed 25 km/hr in 3 seconds. 25 km/hr is about 7 meters/sec.

So, the acceleration due to the brakes is 25/7=3.6 m/sec^2.

Now remembering that F=ma

you can solve for the braking force if you know the car mass.

If you get your units converted correctly your force will be in Newtons.

This is just one way to make an estimate based on something that is fairly easy to measure.

Answer 2

F = ma = kN; where m = car mass = W/g, a = deceleration of mass during braking, k = coefficient of friction (rolling or sliding depending on how you brake), N = normal weight of the car = W since we presume a level driving condition.

F is the braking force. Thus, you can find it by measuring the rate of deceleration (a) and use that in F = ma. Or you can measure k and simply use F = kN to calculate the braking force. Of course you also need to know the weight (N = W) of the car and that g = 9.81 m/sec^2 or 32.2 ft/sec^2 to figure out the mass.

The source of the braking is of course friction of the tires on the road. The car brakes stop the rotation of the braked tires, but it's the friction that stops the car. If you don't believe this, then you obviously have never tried to stop a car on black ice where there is little, if any, friction.

If one has ABS, the car will keep the tires rolling a bit so that the rolling friction coefficient should be used in F = kN. But if it does not have ABS and you lock your brakes, the sliding friction k should be used. The reason ABS keeps the brakes from locking is that rolling k > sliding k; so there is more braking force when the tires are not sliding across the asphalt.

Answer 3

Braking Force

Answer 4

Try this string on your search engine: "physics of auto brakes". It's a compicated subject, but I thought the web site I visited had a good explanation:

http://autopedia.com/stuttgart-west/Physics/StuttPhysics01.html

Answer 5

mass of the vehicle*velocity of the vehicle/time requried to stop
mv/t=n