How far will the block slide before it comes to a stopper far will

Question

A block of mass 13.6 kg is sliding at an initial velocity of 4.65 m/s along a horizontal surface to the right. The surface has a coefficient of friction of 0.254. How far will the block slide before it comes to a stopper fat will 

Answer 1

What do you mean by "it comes to a stopper fat will" ?  I assume you meant to say it comes to complete stop.  Use the kinematic relationship

 

v_f² - v_i² = 2ax

 

and Newton's 2nd law.

 

v_f = 0

v_i = 4.65 m/s

a = F/m = -μmg/m = -μg  [minus sign because the acceleration is opposite the direction of motion]

 

0 - v_i² = 2(-μg)x

 

x = v_i² / (2μg) = (4.65)² [2(0.254)(9.8)] m ≅ 4.343 m

 

Note it does not depend on the mass.