Solve this physics exercise

The forces acting on the block are:

• Gravitational force ($mg$) acting vertically downwards.
• Normal force ($N$) acting perpendicular to the inclined plane.
• Kinetic frictional force ($f_k$) acting parallel to the inclined plane, opposing the motion (up the plane).

The component of gravitational force parallel to the plane is $mg \sin\theta$.
The component of gravitational force perpendicular to the plane is $mg \cos\theta$.

Since there is no acceleration perpendicular to the plane, the net force in this direction is zero.

Therefore, the normal force is:

The kinetic frictional force is given by $f_k = \mu_k N$.
Substitute the expression for $N$:

The block is sliding down the plane, so the net force down the plane causes the acceleration.

Substitute the expression for $f_k$:

Divide the entire equation by $m$:

Factor out $g$:

Given:
$m = 2.0 \text{ kg}$
$\theta = 30^\circ$
$\mu_k = 0.20$
$g = 9.8 \text{ m/s}^2$ (standard acceleration due to gravity)

We know that $\sin(30^\circ) = 0.5$ and $\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$.

Rounding to two significant figures:

The acceleration of the block is $\text{3.2 m/s}^2$.