To find the mass of the wagon, we can use Newton's second law of motion, which states [tex]\( F = m \cdot a \)[/tex], where:
- [tex]\( F \)[/tex] is the net force acting on the object,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration of the object.
Given values:
- Acceleration [tex]\( a = 1.3 \, \text{m/s}^2 \)[/tex],
- Friction force [tex]\( F_{\text{friction}} = 75 \, \text{N} \)[/tex],
- Force exerted by Thunder [tex]\( F_{\text{Thunder}} = 1000 \, \text{N} \)[/tex],
- Force exerted by Misty [tex]\( F_{\text{Misty}} = 800 \, \text{N} \)[/tex].
First, calculate the total pulling force [tex]\( F_{\text{pulling}} \)[/tex]:
[tex]\[ F_{\text{pulling}} = F_{\text{Thunder}} + F_{\text{Misty}} \][/tex]
[tex]\[ F_{\text{pulling}} = 1000 \, \text{N} + 800 \, \text{N} \][/tex]
[tex]\[ F_{\text{pulling}} = 1800 \, \text{N} \][/tex]
Next, calculate the net force acting on the wagon [tex]\( F_{\text{net}} \)[/tex]:
[tex]\[ F_{\text{net}} = F_{\text{pulling}} - F_{\text{friction}} \][/tex]
[tex]\[ F_{\text{net}} = 1800 \, \text{N} - 75 \, \text{N} \][/tex]
[tex]\[ F_{\text{net}} = 1725 \, \text{N} \][/tex]
Now use Newton's second law to find the mass [tex]\( m \)[/tex] of the wagon:
[tex]\[ F_{\text{net}} = m \cdot a \][/tex]
[tex]\[ m = \frac{F_{\text{net}}}{a} \][/tex]
[tex]\[ m = \frac{1725 \, \text{N}}{1.3 \, \text{m/s}^2} \][/tex]
Calculate the mass:
[tex]\[ m = \frac{1725}{1.3} \][/tex]
[tex]\[ m \approx 1326.92 \, \text{kg} \][/tex]
Round the mass to the nearest whole number:
[tex]\[ m \approx 1327 \, \text{kg} \][/tex]
Therefore, the mass of the wagon is [tex]\( \boxed{1327} \)[/tex] kg.
