Question

A skateboarder is attempting to make a circular arc of radius r = 16 m in a parking lot. The total mass of the skateboard and skateboarder is m = 82 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.63.
What is the maximum speed, in meters per second, he can travel through the arc without slipping?

Answer 1

To solve this problem we will apply the concepts related to the centripetal force, for which it is necessary to equate it with the static friction force of the body. From this, we will clear the speed and replace with the given values. Our values are defined as,

$r = 16m$

$m = 82kg$

$\mu_s = 0.63$

Maximum velocity can be find out using centripetal force,

$F_c = \frac{mv^2}{r}$

Must be equal to,

$\frac{mv^2}{r} = \mu_s mg$

$v = \sqrt{\mu_s gr}$

$v = \sqrt{(0.63)(9.8)(16)}$

$v = 9.93m/s$

Therefore the maximum speed that he can travel through the arc without slipping is 9.93m/s