Answer:
\(56.3^{\circ}\)
Explanation:
The figure is missing, find it in attachment.
The figure shows the velocity along the x-axis, \(v_x\), versus time. The slope of the line gives us the acceleration along the x-axis, which is therefore given by:
\(a_x = \frac{\Delta v_x}{\Delta t}=\frac{5-2}{3-2}=3 m/s^2\)
Now we can apply Newton's second law along the x-axis:
\(F_x = m a_x\)
where
\(F_x\) is the resultant force along the x-axis
m = 4 kg is the mass of the disk
\(a_x = 3 m/s^2\) is the acceleration along this axis
Solving,
\(F_x = (4)(3)=12 N\)
So now we know that this is the component of resultant force along the x-axis. The resultant force is given by two forces:
F1, which acts along the x-direction
F2, which acts at a certain angle \(\theta\)
So the component of the resultant along the x-axis can be written as
\(F_x = F_1 + F_2 cos \theta\)
where we know:
\(F_1 = 7 N\\F_2 = 9 N\)
Solving for \(\theta\), we find:
\(cos \theta = \frac{F_x-F_1}{F_2}=\frac{12-7}{9}=0.555\\\theta =cos^{-1}(0.555)=56.3^{\circ}\)
