Answer :
We are given:
- Mass: [tex]$m = 18.0\,\text{kg}$[/tex]
- Applied force: [tex]$F_{\text{applied}} = -235\,\text{N}$[/tex] (the negative sign indicates its direction)
- Friction force: [tex]$F_{\text{friction}} = +163\,\text{N}$[/tex] (opposite to the direction of the applied force)
Step 1: Calculate the net force
Add the forces to find the net force acting on the object:
[tex]$$
F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} = (-235\,\text{N}) + (163\,\text{N}) = -72\,\text{N}.
$$[/tex]
Step 2: Determine the acceleration
Using Newton's second law, [tex]$F = m \cdot a$[/tex], we can solve for the acceleration [tex]$a$[/tex]:
[tex]$$
a = \frac{F_{\text{net}}}{m} = \frac{-72\,\text{N}}{18.0\,\text{kg}} = -4.0\,\text{m/s}^2.
$$[/tex]
Thus, the acceleration of the mass is:
[tex]$$
\boxed{-4.0\,\text{m/s}^2}.
$$[/tex]
- Mass: [tex]$m = 18.0\,\text{kg}$[/tex]
- Applied force: [tex]$F_{\text{applied}} = -235\,\text{N}$[/tex] (the negative sign indicates its direction)
- Friction force: [tex]$F_{\text{friction}} = +163\,\text{N}$[/tex] (opposite to the direction of the applied force)
Step 1: Calculate the net force
Add the forces to find the net force acting on the object:
[tex]$$
F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} = (-235\,\text{N}) + (163\,\text{N}) = -72\,\text{N}.
$$[/tex]
Step 2: Determine the acceleration
Using Newton's second law, [tex]$F = m \cdot a$[/tex], we can solve for the acceleration [tex]$a$[/tex]:
[tex]$$
a = \frac{F_{\text{net}}}{m} = \frac{-72\,\text{N}}{18.0\,\text{kg}} = -4.0\,\text{m/s}^2.
$$[/tex]
Thus, the acceleration of the mass is:
[tex]$$
\boxed{-4.0\,\text{m/s}^2}.
$$[/tex]
