A child slides down a slide with a 30 incline, and at the bottom her speed is pr

Question

A child slides down a slide with a 30 incline, and at the bottom her speed is precisely quarter what it would have been if the slide had been frictionless.

Calculate the coefficient of kinetic friction between the slide and the child.

Constants| Periodic Table Part A A child slides down a slide with a 30° incline, and at the bottom her speed is precisely quarter what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child. Express your answer using two significant figures. Submit Request Answer

Explanation / Answer

here,

theta = 30 degree

let the length of slide be l

when there is no friction

the final speed at the bottom , v1 = sqrt(2 * g * sin(theta) * l)

when friction is present ,

final speed,v2 = v1 /4 = sqrt(2 * g * sin(theta) * l) / 4

accelration , a = ( g * sin(theta) - uk * g * cos(theta))

using third equation of motion

v2^2 - 0 = 2 * a * l

(sqrt(2 * g * sin(theta) * l) / 4)^2 = 2 * ( g * sin(theta) - uk * g * cos(theta)) * l

((2 * sin(theta)) / 16) = 2 * ( sin(theta) - uk * cos(theta))

sin(30) / 16 = ( sin(30) - uk * cos(30))

0.5/16 = 0.5 - uk * cos(30)

solving for uk

uk = 0.54

the coefficient of kinetic friction is 0.54

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