Force Resolver: Split a Force Along Any Two Directions

Force Resolver splits one force into two parts. The two directions can be any lines, perpendicular or not, or the x and y axes, or axes tilted along a ramp. Every part is drawn, and the law of sines or the trigonometry behind it is shown with your numbers.

The numbered parts in Figure 1 are:

1. Picture tabs: each tab is one task; the picture on it shows what the task draws.
2. Drawing: the forces, drawn to scale and updated as you type.
3. Input: the values of the task. Units can be N, kN or lb.
4. Result: the answers, rounded to three significant figures (four when the number starts with 1).
5. How it is worked out: every step of the calculation with your numbers.
6. Scenarios: ready-made real situations; one click fills in the values.

1. Two directions

The force is split along two given lines u and v. The dashed lines through the tip of the force, parallel to each line, show where each part ends.

1. Type the force and the angles of the lines u and v, or drag the force tip and the handles on the lines.
2. Read F_u and F_v; a negative part points the opposite way along its line.
3. The steps use the law of sines in the force triangle.

2. x and y parts

The direction of the force is given by an angle, by a slope (run : rise) or by two points, and the parts take the signs of the quadrant.

1. Choose Angle, Slope or Two points.
2. For a slope, type the run and the rise and pick the quadrant the force points into; the slope triangle is drawn on the force line.
3. Read F_x, F_y and the Cartesian form of the force.

3. Tilted axes

Axes along a ramp (x′) and across it (y′) make incline problems easier.

1. Type the force and the angle of the x′ axis, or move the slider.
2. Read the part along the ramp and the part into it.
3. A negative F_x′ points down the slope.

4. Smallest part

With one direction fixed, the other part is smallest when it is perpendicular to the fixed line.

1. Type the force and the fixed line u; turn the line v with the slider or its handle.
2. Watch the part along v change; the pink dashed line is the shortest possible part.
3. Press Turn v to the smallest part to jump to the answer.

5. Scenarios and phones

The scenarios load a lamp hanging from two wires, a crate on a ramp and the load at the tip of a crane jib. Each scenario opens the right tab and fills in the values, so you can change them and see what happens.

On a phone the drawing comes first and the input, result and steps follow below it. Swipe the picture tabs sideways to see all of them.

6. Tips

• The button with the circular arrow resets the open tab to its starting values; the moon or sun button switches between the light and dark themes.
• Your last values stay in the browser, so the app opens where you left it.
• Angles are measured counterclockwise from +x unless a tab says otherwise.