Question

Can someone help me with college physics question.

Three forces act on a 2.00-kg object at angles theta_1 = 40.0 degree, theta_2 = 60.0degree, and = 20.0degree as shown in Figure 4-29. Find the magnitude of F_2 and F_3 if the magnitude of F_1 is 1.00 N and the acceleration of the object is 1.50 m/s^2 toward the +x direction.

Answer 1

All of the three forces are acting on both axes and there are two unknown forces, so we will get them from both simultaneous equations.

First, let's set the equation on the x-axis:

Now let's set the equation on the y-axis; remember acceleration in this axis is 0, that is the key factor to get the equation:

We have two simultaneous equations:

$F_{2}Cos(60\degree)+F_{3}Cos(20\degree)=2.23N$

$F_{3}Sin(20\degree)-F_{2}Sin(60\degree)=-0.64N$

Solving the system we finally obtain F₂=1.38N and F₃=1.64N