Question

A couch with a mass of 1.00 × 102 kg is placed on an adjustable ramp connected to a truck. As one end of the ramp is raised, the couch begins to move downward. If the couch slides down the ramp with an acceleration of 0.79 m/s2 when the ramp angle is 12.0°, what is the coefficient of kinetic friction between the ramp and the couch? (g = 9.81 m/s2A. 0.47B. 0.55C. 0.39D. 0.35

Answer 1

Answer:$\mu =0.13$

Explanation:

Given

mass of couch $m=1\times 10^2 kg$

acceleration of couch $a=0.79 m/s^2$

inclination $\theta =12^{\circ}$

Let coefficient of kinetic Friction $\mu$

as couch begins to slides Forces act on couch

$mg\sin \theta -f_r=ma$  , where $f_r$ is friction force

$mg\sin \theta -\mu mg\cos \theta =ma$

therefore net acceleration is

$a=g\sin \theta -\mu g\cos \theta$

$0.79=9.8\cdot \sin (12)-\mu g\cos (12)$

$0.08061=0.2079-\mu 0.9781$

$\mu (0.9781)=0.1272$

$\mu =\frac{0.1272}{0.9781}$

$\mu =0.13$