How Far Does a Block Slide Up a Ramp Before Stopping?

[getty102]

Homework Statement

A block of mass 2.96 kg is sliding up a ramp with an initial speed of 12.8 m/s. The ramp is inclined from the horizontal at an angle of 36.4 degrees and the coefficient of kinetic friction is $\mu$=045. What is the displacement of the block along the ramp from the initial time until it stops?

Homework Equations

W=ΔE
W=∫F*ds
ΔE=(m/2)(v_f)²-(m/2)(v₀)² where (v_f)=0
$\Phi$=36.4
m=2.96kg
v₀=12.8 m/s
$\mu$= 0.45

The Attempt at a Solution

$\mu$*m*g*cos$\Phi$x=-(m/2)(v₀)²
solve for x
x=-(m/2)(v₀)²/$\mu$*m*g*cos$\Phi$

 

[tiny-tim]

hi getty102!

correct method, but you forgot to include the gravitational PE (or gravitational work done)

 

[getty102]

Cool, thank you. The potential energy from gravity is dependent on the height. Which in this problem is kind of what I'm looking for because if I can find the height I would know the total displacement of the block up the ramp.

 

[tiny-tim]

xsinΦ ?