A box with an initial speed of #7 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/7 # and an incline of #( 5 pi )/12 #. How far along the ramp will the box go?

1 Answer
Jan 15, 2018

Answer:

The distance is #=2.17m#

Explanation:

Resolving in the direction up and parallel to the plane as positive #↗^+#

The coefficient of kinetic friction is #mu_k=F_r/N#

Then the net force on the object is

#F=-F_r-Wsintheta#

#=-F_r-mgsintheta#

#=-mu_kN-mgsintheta#

#=mmu_kgcostheta-mgsintheta#

According to Newton's Second Law

#F=m*a#

Where #a# is the acceleration

So

#ma=-mu_kgcostheta-mgsintheta#

#a=-g(mu_kcostheta+sintheta)#

The coefficient of kinetic friction is #mu_k=5/7#

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

The incline of the ramp is #theta=5/12pi#

#a=-9.8*(5/7cos(5/12pi)+sin(5/12pi))#

#=-11.28ms^-2#

The negative sign indicates a deceleration

We apply the equation of motion

#v^2=u^2+2as#

#u=7ms^-1#

#v=0#

#a=-11.28ms^-2#

#s=(v^2-u^2)/(2a)#

#=(0-49)/(-2*11.28)#

#=2.17m#