A box of mass 26 kg is sliding down a rough surface incline that makes an angle of 27 degrees with the horizontal. The coefficient of kinetic friction between the box and the surface is 0.36. Resolve the gravitational force into x and y components along the rotated coordinate system.

Question

Physics

Tristin Arias

4 August, 13:05

A box of mass 26 kg is sliding down a rough surface incline that makes an angle of 27 degrees with the horizontal. The coefficient of kinetic friction between the box and the surface is 0.36. Resolve the gravitational force into x and y components along the rotated coordinate system.

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Answers (1)

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Wilkinson · Answer 1

X component 227.03 N

Y component 115.7 N

Explanation:

mass, m = 26 kg

angle of inclination, θ = 27°

coefficient of friction, μ = 0.36

The gravitational force is the weight of the box.

F = mg = 26 x 9.8 = 254.8 N

The x component of the gravitational force is along the inclined plane and it is equal to = F Cos θ = 254.8 Cos 27° = 227.03 N

The y component of the gravitational force is perpendicular to the inclined plane and it is equal to = F Sin θ = 254.8 Sin 27° = 115.7 N