Motorcycle Accident - Coefficient of Friction issues

[pmoon.pt]

Hi Everyone,

I'm trying to find the initial speed of a motorcycle that was involved in an accident. The driver lost control and the bike dragged along the asphalt for some distance. I know several variables but my physics is not a strong suit to say the least. Any help would be much appreciated!

Here is what I know:

- bike traveled on its side (independently of the driver) for 200 meters
- nothing but the friction of the road brought the bike to a stop
- grade of the road - uphill approx 10 degrees
- motorbike weight - approx 145 kg
- dry road
- coefficient of friction of asphalt?

I'd like to know several things:
- the initial speed
- the formula used to find the initial speed
- if the type (i.e. rubber vs metal vs plastic) of contact points and actual surface area of the contact points of the bike on the asphalt make a difference for this calculation and if so how would that factor into the formula? Negligible? Can reasonable assumptions be made for a reasonably accurate initial speed?

Thanks in advance!

 

[AlephZero]

You could get an estimate of the minimum bike speed by assuming no friction at all.

The bike climbs 200 x sin 10 degrees = about 35 meters

The starting speed to "free wheel" up the hill is given by v = sqrt(2gh) = 26 m/s or about 60 mph minimum.

I don't think you can do much more than that, without a lot more information.

Note: when you say "grade: uphill about 10 degrees" are you sure about that? That's a very steep hill. If you mean the grade is "10:1" that would reduce the speed estimate to about 45 mph minimum.

 

[pmoon.pt]

Thanks Aleph, that's very helpful!

Yes I meant 10:1

 

[haruspex]

The frictional aspect is likely to be the more important. Based on various other metal/nonmetal combinations, if the road was clean and dry I would expect a coefficient of around .4 to .5. Let's say it was at least .3. With a gradient of 0.1, that makes it three times as significant. v = sqrt(2gd(0.1+0.3)) = sqrt(2*10*200*0.4) m/s = 40 m/s = 90mph. Any chance of getting a better estimate for mu?

 

[PJC01]

Dear colleague,

Thank you for reaching out for assistance with this problem. I can provide some insights and potential solutions for determining the initial speed of the motorcycle involved in the accident.

To start, we need to understand the concept of coefficient of friction, which is a measure of the amount of friction between two surfaces in contact. In this case, we are concerned with the coefficient of friction between the asphalt and the bike's tires. This value will depend on several factors such as the type of asphalt and the condition of the tires. As you mentioned, the coefficient of friction for asphalt can vary, but a reasonable estimate would be around 0.7-0.8 for dry roads.

To determine the initial speed of the motorcycle, we can use the equation: v^2 = u^2 + 2as, where v is the final velocity (which is zero in this case), u is the initial velocity, a is the acceleration (due to friction), and s is the distance traveled (200 meters). Rearranging this equation, we get u = √(2as).

Now, we need to determine the acceleration due to friction. This can be calculated using the formula: a = μg, where μ is the coefficient of friction and g is the acceleration due to gravity (which is 9.8 m/s^2). Therefore, the acceleration due to friction in this case would be approximately 6.86 m/s^2 (0.7 x 9.8).

Next, we need to consider the effect of the uphill grade of 10 degrees. This will add an additional force acting against the motion of the motorcycle, resulting in a decrease in the initial speed. To account for this, we can use the formula: a = g sin θ, where θ is the angle of the grade. In this case, the acceleration due to the uphill grade would be approximately 1.7 m/s^2 (9.8 x sin 10).

Combining these two accelerations, we get a total acceleration of approximately 8.56 m/s^2 (6.86 + 1.7). Plugging this value into the initial velocity equation, we get u = √(2 x 8.56 x 200) = 26.3 m/s or 94.7 km/h.

As for the type and surface area of the contact points, these factors can certainly have