# Forces on a Bike

1. Apr 17, 2005

### Naeem

A biology student rides her bike around a corner of radius 24 meter at a steady speed of 8.3 m/sec. The combined mass of the student and the bike is 87 kg. The coefficent of static friction between the bike and the road is μs = 0.39.

a) If she is not skidding, what is the magnitude of the force of friction on her bike from the road?
Ffric = N *
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b) What is the minimum value the coefficient of static friction can have before the bike tire will skid?
μmin = *
0.292 OK
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c) What is the magnitude of the total force between the bike tire and the road?
Ftotal = N
1103.19 NO

Need help with part c.

Is it something like this F = mg + mv^2/R

Is this correct.

2. Apr 17, 2005

### Andrew Mason

The total force on the bicycle is:

$$\vec F = m\vec g + \vec N + \mu_sN\hat r = m\vec a = \frac{mv^2}{R}\hat r$$

The forces exerted by the road on the bicycle are $\vec N, \mu_sN\hat r$. The magnitude of those forces would be the magnitude of the vector sum:

$$m\vec g - \frac{mv^2}{R}\hat r = \vec N + \mu_sN\hat r$$

Note$\vec N$ and $\hat r$ are perpendicular. What is the magnitude of the resultant force?

AM