Assuming for now that 6.0m/s2 is the required acceleration for the motorcycle, t

Question

Assuming for now that 6.0m/s2 is the required acceleration for the motorcycle, the next question is whether the motorcycle's tires have enough traction to make that acceleration possible. The mass of motorcycle and rider is 860kg and the coefficient of the static friction force between the motorcycle's tires and the ramp is .75. Assuming the ramp is tilted 9.0 degrees above the horizontal and air resistance is negligible is there enough static friction between the motorcycle's tires and the ramp to give the motorcycle an acceleration of 6.0m/s2?

Explanation / Answer

I am assuming that the motorcycle is trying to climb the ramp. In that case, in a free body diagram, The net force must equal ma. (F = ma)

Since we are trying to climb the ramp, a component of friction and a component of the weight will act down the incline.

Ff = Fn   The normal force on an incline is mgcos

The component of the weight acting down the incline is mgsin

Thus

mgsin + mgcos = ma   (Note m cancels)

Therefore, the mimimum value for = (a - gsin)/gcos

Minimum = (6 - (9.8)(sin9))/(9.8)(cos9)

Minimum = .461

Since is given as .75, it is sufficient to allow for this acceleration.

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