A box with an initial speed of #4 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/4 # and an incline of #(3 pi )/4 #. How far along the ramp will the box go?

1 Answer
Aug 10, 2018

Answer:

The distance is #=0.51m#

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 of Motion

#F=m*a#

Where #a# is the acceleration of the box

So

#ma=-mu_kgcostheta-mgsintheta#

#a=-g(mu_kcostheta+sintheta)#

The coefficient of kinetic friction is #mu_k=5/4#

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

The incline of the ramp is #theta=pi-3/4pi=1/4pi#

The acceleration is #a=-9.8*(5/4cos(1/4pi)+sin(1/4pi))#

#=-15.59ms^-2#

The negative sign indicates a deceleration

Apply the equation of motion

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

The initial velocity is #u=4ms^-1#

The final velocity is #v=0#

The acceleration is #a=-15.59ms^-2#

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

#=(0-16)/(-2*15.59)#

#=0.51m#