# An object, previously at rest, slides #5 m# down a ramp, with an incline of #pi/3 #, and then slides horizontally on the floor for another #2 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

##### 1 Answer

#### Answer:

(I really want someone to double check my work since this is one of my first physics answers)

#### Explanation:

Let's use the top of the ramp for initial condition and bottom of the ramp for final condition.

#PE_i + KE_i = PE_f + KE_f + W_"fric"#

We know that:

#Deltay = 5m(sin(pi/3)) = (5sqrt3)/2#

#KE_i = 0#

#PE_i = mgDeltay = (5sqrt3mg)/2#

#PE_f = 0#

#W_"fric" = 5mu_kF_N = 5mu_kmgcos(pi/3)= 5/2mu_kmgcolor(white)"-"#

So our equation becomes:

#(5sqrt3mg)/2 = KE_f + 5/2mu_kmg#

We can also have another point (

#PE_f + KE_f = PE_"f2" + KE_"f2" + W_"fric2"#

#KE_f = 2mu_kmg#

Substituting this into the first equation gives:

#(5sqrt3mg)/2 = 2mu_kmg + 5/2mu_kmg#

#(5sqrt3)/2 = 9/2mu_k#

#mu_k = (5sqrt3)/9 = 0.9622#

*Final Answer*