Distance Block Slides Up Ramp

getty102

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

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

3. 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$\Phi$

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tiny-tim

Homework Helper
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

Homework Helper
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