Answer:
a. [tex]3.1 m/s^2[/tex]
Explanation:
The equation of the forces along the directions parallel and perpendicular to the slope are:
- Along the parallel direction:
[tex]mg sin \theta - \mu_k R = ma[/tex]
where :
m = 6.0 kg is the mass of the box
g = 9.8 m/s^2 the acceleration of gravity
[tex]\theta=39^{\circ}[/tex] is the angle of the slope
[tex]\mu_k = 0.40[/tex] is the coefficient of friction
R is the normal reaction
a is the acceleration
- Along the perpendicular direction:
[tex]R-mg cos \theta =0[/tex]
From the 2nd equation, we get an expression for the reaction force:
[tex]R=mg cos \theta[/tex]
And substituting into the 1st equation, we can find the acceleration:
[tex]mg sin \theta - \mu_k mg cos \theta = ma[/tex]
Solving for a,
[tex]a=g sin \theta - \mu_k g cos \theta =(9.8)(sin 39^{\circ})-(0.40)(9.8)(cos 39^{\circ})=3.1 m/s^2[/tex]
