How to Calculate Resultant Force: 9 Steps

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-01-15 13:47

The resulting force is the sum of all the forces acting on an object taking into account their intensity, direction and direction (vector sum). An object with a resultant force of zero is stationary. When there is no balance between the forces, ie the resulting one is greater or less than zero, the object is subjected to acceleration. Once the intensity of the forces has been calculated or measured, it is not difficult to combine them to find the resulting one. By drawing a simple diagram, making sure that all vectors are correctly identified in the right direction and direction, the calculation of the resulting force will be a breeze.

Steps

Part 1 of 2: Determine the Resultant Strength

Step 1. Draw a free body diagram

It consists of the schematic representation of an object and of all the forces that act on it taking into account their direction and direction. Read the proposed problem and draw the diagram of the object in question together with the arrows that represent all the forces to which it is subjected.

For example: calculate the resulting force of an object with a weight of 20 N placed on a table and pushed to the right by a force of 5 N, which nevertheless remains stationary because it is subjected to a friction equal to 5 N

Step 2. Establish the positive and negative directions of the forces

By convention, it is established that vectors directed up or to the right are positive, while those directed down or to the left are negative. Remember that it is possible for several forces to act in the same direction and in the same direction. Those that act with the opposite direction always have the opposite sign (one is negative and the other positive).

• If you are working with multiple force diagrams, make sure you are consistent with the directions.
• Label each vector with the corresponding intensity without forgetting the "+" or "-" signs, according to the direction of the arrow you drew on the diagram.
• For example: the force of gravity is directed downwards, so it is negative. The normal upward force is positive. A force that pushes to the right is positive, while the friction that opposes its action is directed to the left and therefore negative.

Step 3. Label all forces

Be sure to identify all those that affect the body. When an object is placed on a surface, it is subjected to gravity directed downwards (F._g) and to an opposite force (perpendicular to gravity), called normal (F). In addition to these, remember to mark all the forces that are mentioned in the problem description. Express the intensity of each vector force in Newton by writing it next to each label.

• By convention, forces are indicated with a capital letter F and a small subscript letter which is the initial of the name of the force. For example, if there is a frictional force you can indicate it as F_to.
• Force of gravity: F._g = -20 N
• Normal force: F. = +20 N
• Frictional force: F._to = -5 N
• Thrust force: F._s = +5 N

Step 4. Add the intensities of all forces together

Now that you have identified the intensity, direction and direction of each force, you just have to add them together. Write the resultant force equation of (F_r), where F_r is equal to the sum of all the forces acting on the body.

For example: F._r = F_g + F + F_to + F_s = -20 + 20 -5 + 5 = 0 N. Since the resultant is zero, the object is stationary.

Part 2 of 2: Calculate the Diagonal Force

Step 1. Draw the force diagram

When you have a force acting diagonally on a body, you need to find its horizontal component (F._x) and vertical (F_y) to calculate the intensity. You will need to use your knowledge of trigonometry and the vector angle (typically called θ "theta"). The vector angle θ is always measured in a counterclockwise direction starting from the positive semiaxis of the abscissa.

• Draw the force diagram respecting the vector angle.
• Draw an arrow according to the direction in which the force is applied and also indicate the correct intensity.
• For example: draw a pattern of a 10 N object being subjected to a force directed up and to the right at a 45 ° angle. The body is also subject to a leftward friction of 10 N.
• The forces to consider are: F_g = -10 N, F = + 10 N, F_s = 25 N, F_to = -10 N.

Step 2. Calculate the F components_x and F_y using the three basic trigonometric ratios (sine, cosine and tangent).

Considering the diagonal force as the hypotenuse of a right triangle, F_x and F_y like the corresponding legs, you can proceed to the calculation of the horizontal and vertical component.

• Remember that: cosine (θ) = adjacent side / hypotenuse. F._x = cos θ * F = cos (45 °) * 25 = 17, 68 N.
• Remember that: sinus (θ) = opposite side / hypotenuse. F._y = sin θ * F = sin (45 °) * 25 = 17, 68 N.
• Note that there may be multiple diagonal forces acting on a body at the same time, so you will need to calculate the components of each. Next, add up all the values of F._x to obtain all the forces acting on the horizontal plane and all the values of F_y to know the intensity of those acting on the vertical.

Step 3. Draw the force diagram again

Now that you have calculated the vertical and horizontal component of the diagonal force, you can redo the diagram considering these elements. Delete the diagonal vector and propose it again in the form of its Cartesian components, without forgetting the respective intensities.

For example, instead of a diagonal force, the diagram will now show a vertical upward force with intensity 17.68 N and a horizontal force to the right with intensity 17.68 N

Step 4. Add all the forces in the x and y direction

Once the new scheme has been drawn, calculate the resulting force (F_r) by adding together all the horizontal and all the vertical components. Remember to always respect the directions and verses of the vectors throughout the course of the problem.

• For example: horizontal vectors are all forces acting along the x axis, so F_rx = 17.68 - 10 = 7.68 N.
• Vertical vectors are all the forces acting along the y axis, so F_ry = 17.68 + 10 - 10 = 17.68 N.

Step 5. Calculate the intensity of the resulting force vector

At this point you have two forces: one along the ordinate axis and one along the abscissa axis. The intensity of a vector is the length of the hypotenuse of the right triangle formed by these two components. Thanks to the Pythagorean Theorem you can calculate the hypotenuse: F_r = √ (F_rx² + F_ry²).

• For example: F._rx = 7, 68 N and F_ry = 17.68 N;
• Insert the values into the equation: F_r = √ (F_rx² + F_ry²) = √ (7, 68² + 17, 68²)
• Solve: F_r = √ (7, 68² + 17, 68²) = √ (58, 98 + 35, 36) = √94, 34 = 9, 71 N.
• The resulting force intensity is 9.71 N and is directed upward and to the right.