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## Homework Statement

A 50 kg trunk is pulled 6.0 meters up a 30 degree incline at a constant velocity. The coefficient of kenetic friction is .2. What is a) the work done by the applied force, b) the work done by gravity and c) the work done by the frictional force

I set up my x axis in the direction of the incline and my y axis normal to the incline.

[itex]F_N[/itex] normal force

[itex]F_g[/itex] gravity

[itex]F_A[/itex] applied force

[itex]F_f[/itex] frictional force

## Homework Equations

[tex]\sum F = 0[/tex]

[tex]\sum F_x = 0 = F_A - F_f - F_{gx}[/tex]

[tex]\sum F_y = 0 = F_N - F_{gy}[/tex]

[tex] F_N = F_{gy} = F_g \cos 30 = (9.8)(50)(\cos 30) = 420N [/tex]

[tex] F_f = \mu_k F_N = (420)(.2) = 85N[/tex]

[tex] F_A = F_f + F_{gy} = \mu_k F_N + \sin 30 F_g = 85 + (.5)(9.8)(50) = 330N [/tex]

[tex]W_f = f_k \cdot \delta d[/tex]

[tex]W_g = mgh = (9.8)(50)(6 \sin 30) = 1500J[/tex]

[tex]W_f = F \cdot d = (85)(6.0)(\cos 0) = 510J[/tex]

[tex]W_a = F \cdot d = (330)(6.0)(\cos 0) = 2000J[/tex]

However, the answers in the book says that a) 2200J b) 1500J c) 700

I can't seem to find my error. Any suggestions?

## The Attempt at a Solution

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