To determine where the 1.22 came from in this problem, let’s analyze the situation step by step:

1. Force Analysis:
   From the diagram and text:

   • The applied force $F_{\text{app}} = 30 \, \text{N}$
   • Frictional force $F_{\text{friction}} = 6 \, \text{N}$
   • Normal force $F_{\text{N}} = 12 \, \text{N}$ (from $F_{\text{grav}}$, assuming vertical equilibrium)

2. Net Force Calculation:
   The net force acting on the object is given by:
   $F_{\text{net}} = F_{\text{app}} - F_{\text{friction}} = 30 \, \text{N} - 6 \, \text{N} = 24 \, \text{N}$

3. Finding $a$:
   The acceleration is calculated using Newton's Second Law:
   $F_{\text{net}} = m \cdot a \implies a = \frac{F_{\text{net}}}{m}$
   Here, $F_{\text{net}} = 24 \, \text{N}$, and $a$ is solved by dividing $F_{\text{net}}$ by the mass $m$.

4. Where $m = 1.22 \, \text{kg}$:
   The value 1.22 appears to be the mass of the object. This mass may have been given earlier in the problem setup or calculated from other provided data (e.g., using $F_{\text{grav}} = m \cdot g$).

   • From $F_{\text{grav}} = 12 \, \text{N}$, we can calculate the mass $m$:
     $m = \frac{F_{\text{grav}}}{g} = \frac{12}{9.8} \approx 1.22 \, \text{kg}$

Final Confirmation:

The 1.22 comes from dividing the gravitational force ($F_{\text{grav}} = 12 \, \text{N}$) by the acceleration due to gravity ($g = 9.8 \, \text{m/s}^2$), giving the mass of the object $m = 1.22 \, \text{kg}$.

Would you like further clarification or help with the rest of the problem?

Relative Questions:

1. How is $F_{\text{grav}}$ related to mass and gravity?
2. Why does $F_{\text{net}}$ subtract the frictional force from the applied force?
3. Can $a$ change if $m$ or $F_{\text{net}}$ changes? How?
4. What happens if the coefficient of friction is reduced?
5. Why is $F_{\text{N}}$ equal to $F_{\text{grav}}$ in this setup?

Tip:

Always double-check mass by recalculating $F_{\text{grav}}$ from $m$ and $g$ to ensure consistency.