A truck pulls boxes up an incline plane. The truck can exert a maximum force of #2,800 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #5/7 #, what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-05-21T17:29:40

The mass is #=238.6kg#

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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))#

#=2800/(9.8(5/7*cos(3/8pi))+sin(3/8pi))#

#=238.6kg#