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12 hours ago

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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 sk

ateboarder 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?

1 answer:

kicyunya [1K]12 hours ago

3 0

To address this question, we will utilize concepts linked to centripetal force, aligning it with the static frictional force acting on the object. Using this relationship, we can derive the velocity and input the known values. The defined values are:

$r = 16m$

$m = 82kg$

$\mu_s = 0.63$

The maximum velocity can be determined using centripetal force,

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

Should be equal to,

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

$v = \sqrt{\mu_s gr}$

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

$v = 9.93m/s$

As a result, the highest speed achievable through the arc without slipping is 9.93m/s

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Explanation:

Provided Information:

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Calculated Area ( A₁ ) = 4 * π * R² = 4 * 3.14 * 0.12 = 0.180864 m².

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Refer to the attached diagram for enhanced clarity regarding the question.

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