Question is too long, so it's in the explanation box.. Please help!!A package in a warehouse slides down a ramp with an acceleration of 1.1 m/s2.  Find the coefficient of kinetic friction between...

Question is too long, so it's in the explanation box.. Please help!!

A package in a warehouse slides down a ramp with an acceleration of 1.1 m/s2.  Find the coefficient of kinetic friction between the package and the ramp if the ramp is inclined at an angel of 36o below the horizontal.

Coefficient of kinetic friction is________

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the equation that relates the friction force and the normal force, which is perpendicular to the surface of ramp, such that:

`F_f = mu*F_n`

`F_f`  represents the friction force

`F_n`  represents the normal force

You may use the following relation to find the magnitude of friction force, such that:

`F_f = m*a - m*g sin alpha`

`F_f = m*(a - g*sin alpha)`

Since the problem provides the acceleration a of package and the angle the ramp is inclined but it does not provides the mass, yields:

`F_f = m*(a - g*sin alpha) => F_f = m*(1.1 - 9.8*sin 36^o)`

`F_f = mu*F_n`

`F_n = m*g*cos alpha => F_f =mu*m*g*cos alpha`

`mu*m*9.8*cos36^o = m*(1.1 - 9.8*sin 36^o)`

Reducing duplicate factors yields:

`mu*9.8*cos 36^o = (1.1 - 9.8*sin 36^o)`

`mu = |(1.1 - 9.8*sin 36^o)|/(9.8*cos 36^o) => mu = 4.660/7.928`

`mu = 0.587`

Hence, evaluating the coefficient of kinetic friction yields `mu = 0.587.`

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