How to calculate the resultant force of distributed forces

1. The resultant force is the area of trapezoid. As for the action point of resultant force, it should be decomposed into quadrilateral and triangle. Calculate the resultant force and action point respectively. The rectangle is the center position, and the triangle is two-thirds of the middle line. Take the moment at the point of resultant force, and the resultant moment is zero.

2.

The resultant force is a vector, and the addition and subtraction of vectors satisfy the parallelogram rule and triangle rule. That is to use this rule to calculate

when several forces acting on the particle act together, the effect is proced. If the effect is the same as that of a certain force F, then the force F is called the resultant force (equivalent method)

The direction of the force F is the direction after the combination of several forces

If the two forces are not collinear, the direction of diagonal is the direction of resultant force

if the directions of the two forces are the same, then the resultant force is equal to the sum of the two forces and the direction remains unchanged

if the directions of the two forces are opposite, the resultant force is equal to the difference between the two forces, and the direction is the same as that of the larger force

If two forces are equal forces, the resultant force is zero. Σ f = 0

extended data:

component force:

If a force acts on an object, its effect on the motion of the object is equivalent to that of several other forces acting on the object at the same time, then these forces are the components of the original force

for example, when pulling a car on a horizontal plane to move forward, the pulling force used above the syncline can be divided into two components: one is to move the car forward horizontally, and the other is to rece the pressure of the weight on the horizontal plane vertically

the decomposition of force is the inverse operation of the composition of force. The parallelogram rule is also obeyed. If a force acts on an object, its effect on the object is the same as that of several other forces acting on the same object at the same time. These forces are the components of that force

3. Several forces act on an object together, and their effect can be replaced by a force, that is, it can be equivalent to a force. Then this force is the resultant force of those forces. From the mathematical point of view, it is the vector sum of each force. To calculate the resultant force, we need to calculate the vector sum of several forces, that is, we use the parallelogram rule; The resultant force is the vector from the beginning of the first force to the end of the last force

4.

(a)

two equivalent concentrated forces are calculated according to two triangles, and their positions are the centroids of two triangles

MA = (Q * A / 2) (2A / 3) + (Q * B / 2) (a + B / 3)

(b)

two equivalent concentrated forces are calculated according to a triangle and a rectangle, the positions of which are the centroid of triangle and rectangle respectively

MA=(q1*L)(L/2)+((q2-q1)*L)(2L/3)

5. (Q1 + Q2) * L / 2 q1.q2 are the maximum and minimum values of linear load respectively

6. Using the parallelogram rule, the resultant forces of two forces are calculated first, then the resultant forces of the third force and the resultant forces are calculated, and so on

7. If the component force is known, it can be made into a parallelogram,
the diagonal line starting from the action point of the force is the resultant force,
then according to the sine theorem of triangle, the angle can be calculated

8. Combine the two forces to get the resultant force, and combine the resultant force with the third force (using the parallelogram rule)

9. Answer:
θ Is the angle between F1 and F2
f ^ 2 = F1 ^ 2 + F2 ^ 2 + 2F1 * F2 * cos θ<
special case:
the component forces are in the same direction, and the sum is the resultant force.
the component forces are in the opposite direction, and the force on one side subtracts the force on the other side.
when the component forces are perpendicular, the Pythagorean theorem is used.
this depends on the specific situation:

10. In most practical problems, an object is subjected to not only one force, but several forces at the same time. When an object is affected by several forces, we can often work out such a force. The effect of this force is the same as that of the original forces. This force is called the resultant force of those forces. The process or method of finding the resultant force of several forces is called the combination of forces
if several forces act on the same point of the object, or their action lines intersect at the same point, these forces are called copoint forces
experiments show that if the line segment representing two common forces F1 and F2 is used as a parallelogram for the adjacent side, then the magnitude and direction of the resultant force F can be expressed by the diagonal between the two adjacent sides. This is called the parallelogram rule of force
if there are more than two common forces acting on the object, we can also apply the parallelogram rule http://ke..com/view/127993.htm Find out their resultant force: first find out the resultant force of any two forces, and then find out the resultant force of this force and the third force, until all the forces are combined, the final result is the resultant force of these forces
according to the parallelogram of the force, we can see that the magnitude and direction of the resultant force F of the forces F1 and F2 change with the angle between F1 and F2. When the angle is equal to 0 degrees, the forces F1 and F2 are on the same straight line and in the same direction, f = F1 + F2, the magnitude of the resultant force is greater than the sum of the magnitude of the two forces, and the direction of the resultant force is the same as that of the two forces. When the included angle is equal to 180 degrees, the forces F1 and F2 are on the same straight line, but in the opposite direction. F = F1-F2, the magnitude of the resultant force is equal to the difference of the magnitude of the two forces, and the direction of the resultant force is the same as that of the larger of the two forces
forces have both magnitude and direction, and the composition of forces should comply with the parallelogram rule. In physics, a physical quantity like this is called a vector. Force is a vector, and so is velocity. However, physical quantities such as length, mass, time, temperature and energy have only size and no direction, which is called scalar in physics.

the composition of forces follows the rule of parallelogram, and the size and direction of resultant force can be obtained by drawing method. In drawing method, it should be noted that all forces on a graph must adopt the same scale, and the proportion of component force and resultant force should be appropriate, We should distinguish between the virtual and the real. However, this method is not very accurate because of the errors in drawing
force triangle rule: two components are connected end to end, and the directed line connecting the beginning and end is their resultant force, as shown in Figure 1. This method is simplified from the parallel four force rule

the composition of forces follows the rule of parallelogram, and the size and direction of resultant force can be obtained by drawing method. In drawing method, it should be noted that all forces on a graph must adopt the same scale, the proportion of component force and resultant force should be appropriate, and the virtual and real lines should be distinguished. However, this method is not very accurate because of the errors in drawing
force triangle rule: two components are connected end to end, and the directed line connecting the beginning and end is their resultant force, as shown in Figure 1. This method is simplified from the parallel four force rule

the composition of forces follows the rule of parallelogram, and the size and direction of resultant force can be obtained by drawing method. In drawing method, it should be noted that all forces on a graph must adopt the same scale, the proportion of component force and resultant force should be appropriate, and the virtual and real lines should be distinguished. However, this method is not very accurate because of the errors in drawing
force triangle rule: two components are connected end to end, and the directed line connecting the beginning and end is their resultant force. This method is simplified from the parallel four force rule.