The coefficient of friction is 0.39
Explanation:
The equation of the forces along the direction parallel to the incline is the following:
[tex]mg sin \theta - \mu N = ma[/tex] (1)
where
[tex]mg sin \theta[/tex] is the component of the weight parallel to the incline (acting downward), with
m = 50 kg being the mass of the couch
[tex]g=9.8 m/s^2[/tex] (acceleration of gravity)
[tex]\theta=25^{\circ}[/tex] is the angle of the ramp
[tex]\mu N[/tex] is the force of friction, acting up along the plane, with
[tex]\mu[/tex] being the coefficient of friction
N is the normal force
[tex]a=0.70 m/s^2[/tex] is the acceleration
The equation of the forces along the direction perpendicular to the plane is
[tex]N-mg cos \theta = 0[/tex] (2)
where [tex]mg cos \theta[/tex] is the component of the weight perpendicular to the plane
From (2) we find
[tex]N=mg cos \theta[/tex]
And substituting into (1)
[tex]mg sin \theta - \mu mg cos \theta = ma[/tex]
And solving for [tex]\mu[/tex], we find
[tex]\mu = \frac{g sin \theta - a}{g cos \theta}=\frac{(9.8)(sin 25^{\circ}-0.70}{(9.8)(cos 25^{\circ})}=0.39[/tex]
Learn more about inclined planes:
brainly.com/question/5884009
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