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## Homework Statement

A 2 kg. block is pulled up a 22° incline with a force of 10N parallel to the incline. What is μ[itex]_{}k[/itex] if it moves up with constant speed?

## Homework Equations

F[itex]_{}N[/itex] = Normal Force

f[itex]_{}k[/itex] = μ[itex]_{}k[/itex] F[itex]_{}N[/itex]

## The Attempt at a Solution

Forces perpendicular to plane: y-vector component of gravity, mgcos[itex]\theta[/itex] (negative) , normal force, F[itex]_{}N[/itex] (positive)

Forces parallel to plane: applied force, F (up plane) , kinetic frictional force, f[itex]_{}k[/itex] (up plane), and x-vector component of gravity, mgsin[itex]\theta[/itex] (down plane)

F[itex]_{}net[/itex][itex]_{}y[/itex] = F[itex]_{}N[/itex] - mgcos[itex]\theta[/itex] = 0

F[itex]_{}N[/itex] = mgcos[itex]\theta[/itex]

F[itex]_{}net[/itex][itex]_{}x[/itex] = F - mgsin[itex]\theta[/itex] + f[itex]_{}k[/itex] = 0

f[itex]_{}k[/itex] = mgsin[itex]\theta[/itex] - F

μ[itex]_{}k[/itex]mgcos[itex]\theta[/itex] = mgsin[itex]\theta[/itex] - F

μ[itex]_{}k[/itex] = [ mgsin[itex]\theta[/itex] - F ] / [ mgcos[itex]\theta[/itex] ]

μ[itex]_{}k[/itex] = ........

The given answer is μ[itex]_{}k[/itex] = 0.55 but I can not come up with this. Please help, thanks!

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