Answer:
a) [tex]W_{f} = -56.659\,W[/tex], b) [tex]W_{g} = 187.973\,J[/tex], c) [tex]W_{N} = 0\,J[/tex], d) [tex]W_{total} = 131.314\,J[/tex]
Explanation:
a) The friction force is:
[tex]f = \mu_{k}\cdot m\cdot g\cdot \cos \theta[/tex]
The work done by friction is:
[tex]W_{f}=-\mu_{k}\cdot m \cdot g \cdot \cos \theta\cdot \Delta s[/tex]
[tex]W_{f} =- (0.4)\cdot (12\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot (\cos 53^{\textdegree})\cdot (2\,m)[/tex]
[tex]W_{f} = -56.659\,W[/tex]
b) The work done by gravity is:
[tex]W_{g} = m\cdot g \cdot \sin \theta \cdot \Delta s[/tex]
[tex]W_{g} = (12\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot (\sin 53^{\textdegree})\cdot (2\,m)[/tex]
[tex]W_{g} = 187.973\,J[/tex]
c) As normal force has a direction perpendicular to motion direction, the work done is equal to zero:
[tex]W_{N} = 0\,J[/tex]
d) The net work done on the package is:
[tex]W_{total} = W_{f} + W_{g} + W_{N}[/tex]
[tex]W_{total} = -56.659\,J +187.973\,J + 0 J.[/tex]
[tex]W_{total} = 131.314\,J[/tex]
