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 #(5 pi )/8 # and the coefficient of friction is #14/3 #, what is the maximum mass that can be pulled up at one time?

1 Answer
Feb 26, 2018

Answer:

The mass is #=497.2kg#

Explanation:

http://spmphysics.onlinetuition.com.my/2013/06/inclined-plane.html

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

Let the force exerted by the truck be #F=4200N#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N=14/3#

The normal force is #N=mgcostheta#

The angle of the plane is #theta=5/8pi#

The acceleration due to gravity is #g=9.8ms^-2#

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

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

#=4200/(9.8(14/3*cos(5/8pi)+sin(5/8pi))#

#=-497.2kg#