An object, previously at rest, slides $5 m$ $5 m$ down a ramp, with an incline of $\frac{π}{3}$ $pi/3$ , and then slides horizontally on the floor for another $2 m$ $2 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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An object, previously at rest, slides $5 m$ $5 m$ down a ramp, with an incline of $\frac{π}{3}$ $pi/3$ , and then slides horizontally on the floor for another $2 m$ $2 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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Answer 1 · 2017-05-20T18:01:04

(I really want someone to double check my work since this is one of my first physics answers)

$μ_{k} = 0.9622$ $mu_k = 0.9622$

Explanation:

Let's use the top of the ramp for initial condition and bottom of the ramp for final condition.

$P E_{i} + K E_{i} = P E_{f} + K E_{f} + W_{fric}$ $PE_i + KE_i = PE_f + KE_f + W_"fric"$

We know that:

$Deltay = 5m(sin(pi/3)) = (5sqrt3)/2$
$KE_i = 0$
$PE_i = mgDeltay = (5sqrt3mg)/2$
$PE_f = 0$
$W_"fric" = 5mu_kF_N = 5mu_kmgcos(pi/3)= 5/2mu_kmgcolor(white)"-"$

So our equation becomes:

$(5sqrt3mg)/2 = KE_f + 5/2mu_kmg$

We can also have another point ( $f2$ ) at the end of the 2 meters when the block is at rest.

$PE_f + KE_f = PE_"f2" + KE_"f2" + W_"fric2"$

$PE_f, PE_"f2", and KE_"f2"$ are all 0, and $W_"fric2" = 2mu_kmg$

$KE_f = 2mu_kmg$

Substituting this into the first equation gives:

$(5sqrt3mg)/2 = 2mu_kmg + 5/2mu_kmg$

$(5sqrt3)/2 = 9/2mu_k$

$mu_k = (5sqrt3)/9 = 0.9622$

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An object, previously at rest, slides $5 m$ $5 m$ down a ramp, with an incline of $\frac{π}{3}$ $pi/3$ , and then slides horizontally on the floor for another $2 m$ $2 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Explanation:

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An object, previously at rest, slides 5 m5m5 m down a ramp, with an incline of pi/3 π3pi/3 , and then slides horizontally on the floor for another 2 m2m2 m. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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Explanation:

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An object, previously at rest, slides $5 m$ $5 m$ down a ramp, with an incline of $\frac{π}{3}$ $pi/3$ , and then slides horizontally on the floor for another $2 m$ $2 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?