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Answer :
We start by determining the net force acting on the mass. The mass experiences two forces: an applied force and a friction force. The applied force is given as
[tex]$$
F_{\text{applied}} = -235\, \text{N}
$$[/tex]
and the friction force is
[tex]$$
F_{\text{friction}} = +163\, \text{N}.
$$[/tex]
The net force is the sum of these two forces:
[tex]$$
F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} = -235\, \text{N} + 163\, \text{N} = -72\, \text{N}.
$$[/tex]
Next, we use Newton's second law, which states that
[tex]$$
F_{\text{net}} = m a,
$$[/tex]
where [tex]$m$[/tex] is the mass and [tex]$a$[/tex] is the acceleration. We can solve for the acceleration by rearranging the equation:
[tex]$$
a = \frac{F_{\text{net}}}{m}.
$$[/tex]
The mass is provided as [tex]$18.0\, \text{kg}$[/tex], so substituting the known values gives
[tex]$$
a = \frac{-72\, \text{N}}{18.0\, \text{kg}} = -4.0\, \text{m/s}^2.
$$[/tex]
The negative sign for the acceleration indicates that the acceleration is in the opposite direction to the positive reference direction (as defined by the problem setup).
Thus, the acceleration of the mass is
[tex]$$
a = -4.0\, \text{m/s}^2.
$$[/tex]
[tex]$$
F_{\text{applied}} = -235\, \text{N}
$$[/tex]
and the friction force is
[tex]$$
F_{\text{friction}} = +163\, \text{N}.
$$[/tex]
The net force is the sum of these two forces:
[tex]$$
F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} = -235\, \text{N} + 163\, \text{N} = -72\, \text{N}.
$$[/tex]
Next, we use Newton's second law, which states that
[tex]$$
F_{\text{net}} = m a,
$$[/tex]
where [tex]$m$[/tex] is the mass and [tex]$a$[/tex] is the acceleration. We can solve for the acceleration by rearranging the equation:
[tex]$$
a = \frac{F_{\text{net}}}{m}.
$$[/tex]
The mass is provided as [tex]$18.0\, \text{kg}$[/tex], so substituting the known values gives
[tex]$$
a = \frac{-72\, \text{N}}{18.0\, \text{kg}} = -4.0\, \text{m/s}^2.
$$[/tex]
The negative sign for the acceleration indicates that the acceleration is in the opposite direction to the positive reference direction (as defined by the problem setup).
Thus, the acceleration of the mass is
[tex]$$
a = -4.0\, \text{m/s}^2.
$$[/tex]
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