Question

the object in this diagram has a mass of 4 kg. according to this diagram, what is the acceleration of this object?
0 m/s²
2 m/s²
9 m/s²
32 m/s²
f_norm = 20n
f_frict = 14n
f_app = 22n
f_grav = 20n

Explanation:

Step1: Calculate net - force in x - direction

The forces in the x - direction are the applied force $F_{app}=22N$ and the frictional force $F_{frict}=14N$. The net - force in the x - direction $F_{net,x}=F_{app}-F_{frict}$.
$F_{net,x}=22 - 14=8N$
The forces in the y - direction are the normal force $F_{norm}=20N$ and the gravitational force $F_{grav}=20N$. The net - force in the y - direction $F_{net,y}=F_{norm}-F_{grav}=20 - 20 = 0N$. So the overall net - force $F_{net}=F_{net,x}=8N$.

Step2: Use Newton's second law

Newton's second law is $F = ma$, where $F$ is the net - force, $m$ is the mass, and $a$ is the acceleration. We know $F_{net}=8N$ and $m = 4kg$. We can solve for $a$ by rearranging the formula to $a=\frac{F_{net}}{m}$.
$a=\frac{8}{4}=2m/s^{2}$

Answer:

$2m/s^{2}$