Weight of vehicles when stopping

[Probie]

Homework Statement

Is it possible that a vehicle weighing 2000 kg and a vehicle weighing 13000 kg can both use the same skid to stop formula?? Does the difference in weight not come into account?

Homework Equations

Where :
S = speed in km/h
µ = .75
d = skid distance

S = 15.9 *( sgr ( µ d ))

The Attempt at a Solution

I know how to do the above equation. It is the derivation I do not know how to do.
in order to prove or disprove the weight effect on the speed.

 

[Probie]

solved myself

Thanks, but I proved this one myself, with the use of kinetic energy. But if someone would like to check this over to make sure I am correct I would appreciate it.

13000 kg vehicle leaves skid marks 21 meters long, the drag factor is .7

13000 * 21 * .7 = 191100 joules

V = sqr ((2gKE)/w)
V = sqr ((2* 9.81*191100))/13000)
V = sqr (3749382/13000)
V = sqr 288.414
V = 16.98 m/s
S = 16.98 / .2777
S = 61.14 km/h

2000 kg vehicle leaves skid marks 21 meters long, the drag factor is .7

2000 * 21 * .7 = 29400 joules

V = sqr ((2gKE)/w)
V = sqr ((2* 9.81*29400))/2000)
V = sqr (576828/2000)
V = sqr 288.414
V = 16.98 m/s
S = 16.98 / .2777
S = 61.14 km/h

Check skid to stop

S = sqr (254 µ d ))
S = sqr (254 * .7 * 21))
S = sqr 3733.8
S = 61.10 km/h

 

[m2003]

I would like to clarify that the equation provided in the homework statement is not a skid to stop formula, but rather an equation that calculates the speed at which a vehicle will skid to a stop based on the coefficient of friction (µ) and the skid distance (d).

To answer the question, it is possible for two vehicles of different weights to use the same skid to stop formula. This is because the equation only takes into account the coefficient of friction and the skid distance, not the weight of the vehicle. However, the weight of the vehicle can affect the skid distance and ultimately, the stopping distance.

In general, a heavier vehicle will require a longer skid distance to come to a stop compared to a lighter vehicle due to its greater inertia. This means that the weight of the vehicle does come into account in terms of the stopping distance, but not in the equation provided.

In order to accurately determine the effect of weight on the stopping distance, a more comprehensive formula would need to be used, taking into account factors such as the vehicle's weight, speed, braking force, and road conditions. This type of formula would require more complex calculations and would likely vary depending on the specific vehicle and situation.

In summary, while the equation provided can be used for both vehicles, it does not fully account for the effect of weight on the stopping distance. It is important to consider other factors and use a more comprehensive formula for a more accurate analysis.