An object, previously at rest, slides $5 m$ $5 m$ down a ramp, with an incline of $\frac{3 π}{8}$ $(3pi)/8$ , and then slides horizontally on the floor for another $12 m$ $12 m$ . 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 $\frac{3 π}{8}$ $(3pi)/8$ , and then slides horizontally on the floor for another $12 m$ $12 m$ . 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 · 2016-03-11T14:05:16

$= 0.33$ $=0.33$

Explanation:

slant height of the ramp $l = 5 m$ $l=5m$
Angle of inclination of the ramp $θ = 3 \frac{π}{8}$ $theta = 3pi/8$
Length of horizontal floor $s = 12 m$ $s=12m$
vertical height of the ramp $h = l \cdot sin θ$ $h =l*sintheta$
Mass of the object = m
Now applying conservation of energy

Initial PE = work done against friction
$m g h = μ m g cos θ \times l + μ m g \times s$ $mgh=mumgcostheta xxl+mumg xxs$
$\Rightarrow h = μ cos θ \times l + μ \times s$ $=>h=mucostheta xxl+mu xxs$
$\Rightarrow μ = \frac{h}{l cos θ + s} = \frac{l sin θ}{l cos θ + s} = \frac{5 \times sin (3 \frac{π}{8})}{5 cos (3 \frac{π}{8}) + 12} = \frac{4.62}{13.9} = 0.33$ $=>mu=h/(lcostheta+s)=(lsintheta)/(lcostheta+s)=(5xxsin(3pi/8))/(5cos(3pi/8)+12)=4.62/13.9=0.33$

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An object, previously at rest, slides $5 m$ $5 m$ down a ramp, with an incline of $\frac{3 π}{8}$ $(3pi)/8$ , and then slides horizontally on the floor for another $12 m$ $12 m$ . 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 5m5 m down a ramp, with an incline of 3π8(3pi)/8 , and then slides horizontally on the floor for another 12m12 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 $5 m$ $5 m$ down a ramp, with an incline of $\frac{3 π}{8}$ $(3pi)/8$ , and then slides horizontally on the floor for another $12 m$ $12 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?