Answer:
2.77 m/s^2
Explanation:
For simplicity, we will say that the x-axis is parallel to the inclined plane and the y-axis is perpendicular to the inclined plane. The force that the surface applies on the block N will be perpendicular to the plane. The force of friction can be expressed like this:
[tex]Fr = u*N[/tex]
Where u is the coefficient of kinetic friction.
The x-component and y-component of the weight force will be:
[tex]W_y = W*cos(37)\\W_x = W*sin(37)[/tex]
In the y-axis, the acceleration of the block is 0. Then:
[tex]N - W_y = 0\\N = W_y = W*cos(37) = m*g*cos(37)[/tex]
In the X-axis, the summation of forces would be:
[tex]W_x - Fr = m*a\\m*g*sin(37) - u*N = m*g*sin(37) - u*m*g*cos(37) = ma\\a = \frac{mg(sin(37)-u*cos(37))}{m} = 9.81m/s^2*(sin(37)-0.4*cos(37))=2.77m/s^2[/tex]
