An object, previously at rest, slides $7 m$ $7 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Question

An object, previously at rest, slides $7 m$ $7 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Impact of this question

1370 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-21T14:23:21

Here length of the ramp (l)= 7m

Angle of inclination of the ramp $θ = \frac{π}{6}$ $theta = pi/6$
Height of the object from horizontal floor, $h = l sin θ$ $h=lsintheta$
If mass of the body is $m k g$ $m kg$
The initial gravitational potential energy of the body $P E = m g h = m g l sin θ = 7 m g sin θ J$ $PE=mgh=mglsintheta=7mgsintheta J$

The normal reaction acting on the body when it is sliding down the ramp is $N_{r} = m g cos θ$ $N_r=mgcostheta$
and the corresponding frictional force $F_{r} = μ N_{r} = μ m g cos θ$ $F_r=muN_r=mumgcostheta$
where $μ =$ $mu=$ coefficient of kinetic friction
work done against frictional force when sliding down the ramp $W_{1} = F_{r} \times l = μ m g cos θ \times 7 J$ $W_1=F_rxxl=mumgcosthetaxx7J$

when the body slides on horizontal force,then normal reaction $N_{f} = m g$ $N_f=mg$ and corresponding frictional force $F_{f} = μ N_{f} = μ m g$ $F_f=muN_f=mumg$
work done against frictional force when sliding 24m along floor
$W_{2} = F_{f} \times 24 = 24 μ m g J$ $W_2=F_fxx24=24mumgJ$

Now applying conservation of mechanical energy we can write

The initial KE being zero
Initial PE = total work done against frictional force $= W_{1} + W_{2}$ $=W_1+W_2$
$:. 7mgsintheta=W_1+W_2$
$=>7mgsintheta=7mumgcostheta+24mumg$
$=>mu=(7sintheta)/(24+7costheta)=(7sin(pi/6))/(24+7cos(pi/6))$
$=(7xx1/2)/(24+7xxsqrt(3)/2)=(3.5)/33~~0.105$

Science

Math

Humanities

... and beyond

An object, previously at rest, slides $7 m$ $7 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

An object, previously at rest, slides 7 m7m7 m down a ramp, with an incline of (pi)/6 π6(pi)/6 , and then slides horizontally on the floor for another 24 m24m24 m. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer

Related questions

Impact of this question

An object, previously at rest, slides $7 m$ $7 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?