Answer :
We start by determining the net force acting on the mass. The total force is the sum of the applied force and the friction force. In equation form, this is:
[tex]$$ F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} $$[/tex]
Substituting the given values:
[tex]$$ F_{\text{net}} = 196\, \text{N} + (-32.0\, \text{N}) = 164.0\, \text{N} $$[/tex]
Next, we use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
[tex]$$ F_{\text{net}} = m \cdot a $$[/tex]
Solving for acceleration ([tex]$a$[/tex]), we get:
[tex]$$ a = \frac{F_{\text{net}}}{m} $$[/tex]
Substitute the known values into the equation:
[tex]$$ a = \frac{164.0\, \text{N}}{41\, \text{kg}} $$[/tex]
Simplifying the expression:
[tex]$$ a = 4.0\, \text{m/s}^2 $$[/tex]
Thus, the acceleration of the mass is:
[tex]$$ a = 4.0\, \text{m/s}^2 $$[/tex]
[tex]$$ F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} $$[/tex]
Substituting the given values:
[tex]$$ F_{\text{net}} = 196\, \text{N} + (-32.0\, \text{N}) = 164.0\, \text{N} $$[/tex]
Next, we use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
[tex]$$ F_{\text{net}} = m \cdot a $$[/tex]
Solving for acceleration ([tex]$a$[/tex]), we get:
[tex]$$ a = \frac{F_{\text{net}}}{m} $$[/tex]
Substitute the known values into the equation:
[tex]$$ a = \frac{164.0\, \text{N}}{41\, \text{kg}} $$[/tex]
Simplifying the expression:
[tex]$$ a = 4.0\, \text{m/s}^2 $$[/tex]
Thus, the acceleration of the mass is:
[tex]$$ a = 4.0\, \text{m/s}^2 $$[/tex]
