Answer:
The acceleration of the sled [tex]a= 2.468 \frac{m}{s^{2} }[/tex]
Explanation:
Using Newton's law the force the tow girls are making pulling the sled get an acceleration so:
[tex]F=m*a[/tex]
However the forces make the system in equilibrium and can find the force total os the system to find the acceleration of the system
∑F=F=0
[tex]m=15kg\\u=0.1\\F1=F2=27N\\[/tex]
∑F=Fj=0
The force F1 is in the same axis so the F2 have component in axis 'y' and F1 in axis 'y' is zero
[tex]N+F2*sin(\alpha)=m*g\\N+27N*sin(30)=15kg*9.8\frac{m}{s^{2} } \\N=15kg*9.8\frac{m}{s^{2} }-27N*sin(30)\\N=133.5N[/tex]
[tex]f=u*N\\f=0.1*133.5N\\f=13.35N[/tex]
The total force is in axis 'x' so:
[tex]Ft=F1+F2*cos(30)-f\\Ft=27N+27N*cos(30)-13.35N\\Ft=37.03[/tex]
[tex]Ft=m*a\\a=\frac{Ft}{m} \\a=\frac{37.03N}{15kg}\\a=2.468 \frac{m}{s^{2} }[/tex]
