Answer:
a) 1.855m/s^2, 9.71\° to the east-north
b) 0.103N, 9.46° to the west-south
Explanation:
To find the acceleration of the system you can assume that the forces are applied in a xy plane, where force toward north are directed in the +y direction, and forces to the east in the +x direction. BY taking into account the components of the acceleration for each axis you obtain the following systems of equations:
[tex]0.06N-0.06Nsin(45\°)=ma_y\\\\0.08N-0.02N+0.06cos(45\°)=ma_x[/tex]
m: mass of the crumb of bread = 0.056kg
you simplify the equations an replace the values of the mass in order to obtain the acceleration components:
[tex]a_y=\frac{0.017N}{0.056kg}=0.313\frac{m}{s^2}\\\\a_x=\frac{0.102N}{0.056kg}=1.829\frac{m}{s^2}[/tex]
[tex]\theta=tan^{-1}(\frac{0.313}{1.829})=9.71\°\\\\a=\sqrt{a_x^2+a_y^2}=\sqrt{(1.829)^2+(0.313)^2}\frac{m}{s^2}=1.855\frac{m}{s^2}[/tex]
then, the acceleration of the system has a magnitude of 1.855m/s^2 and a direction of 9.71\° to the east-north
The fifth force must cancel both x an y components of the previous net force, that is:
[tex]0.06N-0.06Nsin(45\°)+F_y=0\\\\F_y=-0.017N\\\\0.08N-0.02N+0.06cos(45\°)+F_x=0\\\\F_x=-0.102N\\\\\phi=tan^{-1}(\frac{-0.017}{-0.102N})=9.46\°[/tex]
[tex]F=\sqrt{(0.102)^2+(0.017)^2}N=0.103N[/tex]
the, the force needed to reach the equilibrium has a magnitude of 0.103N and a direction of 9.46° to the west-south
