A workman pushes a 40.0 kg crate up an incline. He begins pushing the crate at x

Question

A workman pushes a 40.0 kg crate up an incline. He begins pushing the crate at x = 0 ,
and continues pushing the crate until he has reached x = 3.00 m. As shown in the diagram, the
x-axis is aligned with the incline, and the origin is at the base of the incline. The plot to the right
of the diagram shows the x-component of the workmans push as a function of the x-coordinate.
The plot shows that the workmans push starts at 0N, increases to a strength of 800 N and then
decreases back to zero. The coefficient of kinetic friction between the crate and the plot is 0.20.
(a) Compute the work done on the crate by gravity and by friction.
(b) Compute the work done on the crate by the workman.
(c) Assuming that the crate was initially at rest, what is the speed of the crate when it reaches the
top of the incline?

Explanation / Answer

a)work by gravity=mgh=mg*3*sin35=-40*9.8*3*sin(35 degree)=-674.52J

work by friction=-umg*x*cos35=-0.2*40*9.8*3*cos(35 degree)=-192.66J

b)work by crateman = area under graph=1/2*800*3=1200J

c)KE=work by cateman+work by fricion=work by gravity=1200-192.66-674.52=332.82

1/2*m*v^2=kinetic energy

so v = sqrt(2*m*kinetic energy)=sqrt(2*40*332.82)=163.17m/s

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