An object with a mass of #4 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 5+tanx #. How much work would it take to move the object over #x in [(-5pi)/12, (pi)/4]#, where x is in meters?

Answer 1

As we know that work #= int_(x_1)^(x_2) vecF.vec (dx)# Here #F=4xx10xx (5+tanx)=40xx(5+tanx)# #:.W=int_-((5pi)/12)^(pi/4)40(5+ tanx)dx# #=200xx(pi/4-(-(5pi)/12))+40[lnsec (pi/4)-lnsec (-(5pi)/12)]# Now simplify it...

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Answer 2

Elena Albarran

[ W = \int_{(-5\pi)/12}^{(\pi)/4} \left( \mu_k \cdot m \cdot g \cdot \cos(x) + m \cdot g \cdot \sin(x) \right) ,dx ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.