(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A pig is sliding down a ramp that has an angle of 35 degrees from the horizontal plane. If the friction coefficient was 0 the ride would only take half the time. What is the kinetic friction coefficient between pig and ramp?

2. Relevant equations

F_{net}= ma

v² = u² + 2as

a = [itex]\Delta[/itex]v/t

f_{k}= u_{k}N = u_{k}mgsin[itex]\theta[/itex]

3. The attempt at a solution

Since I wasn't given a length of the ramp, I decide it to be s=10 meters (the length shouldn't matter, I just use the value so I can perform calculations).

u = 0 m/s

s = 10 m

a = gsin[itex]\theta[/itex] = 5.62 m/s²

v = [itex]\sqrt{2as}[/itex] = [itex]\sqrt{2*5.62*10}[/itex] = 10.6 m/s

t = (v-u)/a = 10.6/5.62 = 1.87 s

This is the time it takes without any friction. Now let's double this time, and find the acceleration. Then, through the expressions of the forces, solve for u_{k}:

t = 3.74 s

u = 0 m/s

s = 10 m

v = s/t = 2.67 m/s

a = (v-u)/t = 0.71 m/s²

F = ma = mgsin[itex]\theta[/itex] - u_{k}gcos[itex]\theta[/itex]

Rearrange and you'll get this

u_{k}= [itex]\frac{a + gsin\theta}{gcos\theta}[/itex] = [itex]\frac{0.71 + 9.8sin(35)}{9.8cos(35)}[/itex] = 0.787

This answer isn't correct, but it's rather close (probably by coincidence). Anyhow, can anyone hint me in the right direction? Where am I going wrong?

Thanks

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# Find the kinetic friction coefficient

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