# Physics Question?

When taking a turn, a motocycle driver rides along the arc of a circular road with a radius of 20 m at a constant speed of 10 m/s.

What angle must the rider make in order to round the curve without falling off?

Estimate the max speed with which the curve could be taken.

What is the centripetal force if the rider and the bike is 80 kg?

Thanks!

Relevance

The required centripetal force is

F = mv^2 / r

And it acts towards the centre of the circle NOT along the surface of the road.

In this case the rider leans and the road remains horizontal.

so that the horizontal force is mv^2/r and the vertical force is mg.

If the resulting force lies along the riders body then it is the HYPOTENUSE of the triangle.

so its angle is given by TAN(theta) = opposite / adjacent.

if we measure from the vertical

tan (theta) = (mv^2 / r ) / (mg) = v^2 / ( gr)

theta = atan ( v^2/(gr) ) = atan( 10 ^ 2 /(9.8 * 20) ) = 27 degrees from the vertical.

For part 2 estimate the maximum angle that the rider could be at before the muffler, pegs etc scrape the ground.

Use that in the SAME formula to calculate v

Part 3 depends on the speed. Which of the two answers are you to use? The English is not sufficiently good to determine if they mean "the centripetal force in part 1" or " the centripetal force in part 2"

As it is immediately preceding the question I would be using YOUR answer for part 2 and giving the force for that using the first equation I provided.

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• For a motorcycle to move around an arc of a circle at a constant speed, there must be a centripetal force.

Centripetal acceleration = v^2 ÷ r = 10^2 ÷ 20 = 5 m/s^2

Fc = 80 * 5 = 400 N

Let’s determine the weight of rider and the bike.

Weight = 80 * 9.8 = 784 N

What angle must the rider make in order to round the curve without falling off?

Let θ be the angle from horizontal. Let F

F * sin θ = weight = 80 * 9.8 = 784 N

F * cos θ = Fc = 400

Tan θ = 784 ÷ 400 = 1.96

The angle is approximately 63˚

If the angle is measured from vertical, tan θ = 400 ÷ 784

The angle is approximately 27˚.

I have no idea of how to calculate the maximum speed.

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