physics question

Question

the 2 kg block in the figure slides down a frictionless curved ramp, starting from rest at a height of h=2.0 m the block the slides d= 8.0 m on a rough horizontal surface before coming to rest. what is the coefficient of friction between the block and the horizontal surface

Answer 1

There is no diagram to look at.  If I am interpreting the information correctly, the block slides down without friction, picks up speed, and then slides with friction on a horizontal surface at constant acceleration, and comes to a stop.  For the horizontal part, you can use the kinematic relation

 

v_f² - v_i² = 2ad

 

v_i = speed at the bottom of the incline

 

v_i² = 2gh = 2(9.8)(2.0) (m/s)² = 39.2 (m/s)²

v_f = 0  [full stop]

d = 8.0 m

 

Find "a", get force from "a", and get μ from the force.

 

a = -v_i²/(2d)

 

Working with just the magnitude,

 

|a| = v_i²/(2d)

 

f = force of friction = μmg = ma ⇒

 

μ = |a|/g = [v_i²/(2d)] / g = v_i² / (2gd) = (39.2) / [2(9.8)(8.0)] = 0.25