Question

Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30 N, and the other east and at an angle of 30° upward from horizontal with a tension force of 40 N. Find the components of the net force on the cart.

Answer 1

Given

Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30 N, and the other east and at an angle of 30° upward from horizontal with a tension force of 40 N.

To find

The components of the net force on the cart.

Explanation

For the force 40N

The x-component acting along east is

$40cos30^o=34.64N$

The y-component acting upward is

$40\text{ sin30=20N}$

Total force along x-axis,

$F_x=34.64-30=4.64N$

Total force along upward is

$F_y=20\text{ N}$

Thus, the net force is

$\begin{gathered} F=\sqrt{F_x^2+F_y}^2 \\ \Rightarrow F=\sqrt{4.64^2+20^2} \\ \Rightarrow F=20.52N \end{gathered}$

Conclusion

The net force is 20.52 N