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.

Step-by-step 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=√(F_x^2+F_y)^2 \\ \Rightarrow F=√(4.64^2+20^2) \\ \Rightarrow F=20.52N \end{gathered}`

Conclusion

The net force is 20.52 N