A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,200 N#. If the plane's incline is #pi/8 # and the coefficient of friction is #3/5 #, what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-05-28T06:20:57

The mass is #=457.4kg#

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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))#

#=4200/(9.8(3/5*cos(1/8pi))+sin(1/8pi))#

#=457.4kg#