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A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,500 N#. If the plane's incline is #(7 pi )/8 # and the coefficient of friction is #5/3 #, what is the maximum mass that can be pulled up at one time?

Answer 1

Isabella Alvarez

The mass is #=396.8kg#

Resolving in the direction parallel to the plane #↗^+#

Let the force exerted by the truck be #=FN#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N#

The normal force is #N=mgcostheta#

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

#m=F/(g(mucostheta+sintheta))#

#=4500/(9.8(5/3*cos(7/8pi))+sin(7/8pi))#

#=-396.8kg#

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Answer 2

Nicholas Agrusa

The maximum mass that can be pulled up the incline plane is 686.44 kg.

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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.