Question

A skateboarder is attempting to make a circular arc of radius r = 11 m in a parking lot. The total mass of the skateboard and skateboarder is m = 87 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.62 .
(a) What is the maximum speed, in meters per second, he can travel through the arc without slipping?

Answer 1

Answer:

V = 8.26 m/s

Explanation:

The sum of forces on the centripetal-axis is:

$Ff = m*a_c$

Maximum speed happens when friction force is maximum, so:

$\mu*N = m*V^2/R$

$\mu*m*g = m*V^2/R$

$V=\sqrt{R*\mu*g}$

V = 8.26 m/s

Answer 2

The maximum speed that he can travel through the arc without slipping is mathematically given as

v = 9.93m/s

The maximum speed

Question Parameters:

Generally the equation for the Maximum velocity   is mathematically given as

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

Therefore

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

v = 9.93m/s

Therefore, the maximum speed that he can travel through the arc without slipping is

v = 9.93m/s

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