In this article, you will learn what the resultant force also known as net force is, and how to find it when an object is subject to parallel forces as well as non-parallel forces with the help of examples. When an object is subject to several forces, the resultant force is the force that alone produces the same acceleration as all those forces.

## Force Required to be a minimum

The reason why the resultant force is useful is that it allows us to think about several forces as though they were a single force. This means that to determine the effect that several forces have on an object, we only need to determine the effect that a single force has. If we know the mass m of an object and the acceleration a produced by the forces that act on it, we can find the resultant force using Newton's Second Law. Indeed, according to Newton's Second Law, the force F that alone produces the acceleration a on an object of mass m is:.

Which indicates that the resultant force R has the same direction as aand has magnitude equal to the product m a. For example, if a box of 1. Often, however, we know the forces that act on an object and we need to find the resultant force.

Experiments show that when an object is subject to several forces, F 1F 2Notice that this is not a mere sum of the magnitudes of the forces, but the sum of the forces taken as vectorswhich is more involved because vectors have both a magnitude and a direction that we need to consider when doing the sum.

According to the above equation, if an object is subject to no forces, then the resultant force is zeroand if an object is subject to only one force, then the resultant force is equal to that force. These two cases are pretty simple, but what about an object subject to two or more forces?

How do we perform the vector sum then? To explain this clearly, we will now go through all the cases that can happen, from simple ones in which all the forces are parallel, to more complex ones in which the forces are not parallel, and show how to find the resultant force in each of them with the help of examples.

Let's start with the simple case in which an object is subject to two forces that act in the same direction:. The resultant force is in the same direction as the two forcesand has the magnitude equal to the sum of the two magnitudes :. Let's consider the case in which an object is subject to two forces that act in opposite directions.

The resultant force will be zero because two opposite forces cancel each other out. To find the resultant force in this case, we first sum all the forces that go in one direction, and then all the forces that go in the other direction:.

In the previous cases, we have forces that are all parallel to one another. It's time to consider the case in which an object is subject to two forces that are not parallel. For example, let's assume that we have a block subject to two forces, F 1 and F 2. Since one of the two forces is horizontal, for convenience, we choose the x -axis horizontal, and the y -axis vertical, and we place the origin at the center of our block:.

The next step is to determine the x and y components of all the forces that act on the block :. If we sum all the x components, we will get the x component of the resultant force :. Similarly, if we sum all the y components, we will get the y component of the resultant force :. At this point, we know the x and y components of Rwhich we can use to find the magnitude and direction of R :.

The magnitude of R can be calculated by applying Pythagoras' Theorem :. Finally, let's examine the case in which an object is subject to more than two non-parallel forces. For example, suppose we have an object that is subject to three forces, F 1F 2and F 3. We can find the resultant force R using the same process that we used in the previous case of two non-parallel forces. Then, we determine the x and y components of the individual forces:. Again, the x component of the resultant force R is the sum of all x components:.If the resultant force acting on the bracket is required to be a minimum, determine the magnitude of F1 and the resultant force.

Welcome to Mathskey. Most popular tags solving-equations system-of-equations functions math slope-intercept-form physics homework-help trigonometric-identities integration substitution-method limits elimination-method. Please log in or register to add a comment. Please log in or register to answer this question. Related questions Engineering mechanics statics 13th hibbler chapter 2 problem Engineering mechanics statics 13th hibbler chapter 2 problem Engineering mechanics statics 13th hibbler chapter 2 problem 1.

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View Answer. Determine the magnitude and orientation, measured counterclockwise from the positive y axis, of the resultant force acting on the bracket. Determine the magnitude and orientation, measured clockwise from the positive x axis, of the resultant force of the three forces acting on the bracket. X should be 1 if A has been 1 for at Y should be 1 if A has been 1 for at least two consecutive cycles.

### Force Required to be a minimum

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Solve Problem by summing the rectangular or x. Determine the x and y components of F1 andF2. Discuss the logic underlying the use of three-sigma limits on Shewhart control charts.

How will the chart respond if narrower limits are chosen? How will it respond if wider limits are chosen? Sign In. Get help from Civil Engineering Tutors. Best for online homework instance. Complaint Have any complaint?In mechanics we deal with two types of quantities variables : scalar and vector variables. Scalar variables have only magnitude, for example: length, mass, temperature, time.

Vector variables have magnitude and direction, for example: speed, force, torque. The direction of the vector is defined by the angles of the force witch each axis.

The vector variables are usually represented using bold symbols with arrows on top. Several forces can act on a body or point, each force having different direction and magnitude. In engineering the focus is on the resultant force acting on the body. The resultant of concurrent forces acting in the same plane can be found using the parallelogram lawthe triangle rule or the polygon rule.

Two or more forces are concurrent is their direction crosses through a common point. For example, two concurrent forces F 1 and F 2 are acting on the same point P. In order to find their resultant Rwe can apply either the parallelogram law or triangle rule.

If there are several forces acting on the same point, we can apply the polygon rule to find their resultant. The resultant force can be determined also for three-dimensional force systemsby using the polygon rule. The parallelogram law, triangle rule and polygon rule are geometric methods to find the force resultant.

The law of sines gives the relationship between the forces and the angles :. The resultant force can also be calculated analyticalusing force projections. Using the force projection methodwe can calculate the magnitude and direction angles of the resultant force.

Replacing 4 in the equations above gives the angles with each axis as trigonometric functions :. The force projection method can also be used for co-planar x, y-axis force resultant calculations.

Example 1. Step 1. To get an idea on how the resultant force might look like, we can apply to polygon rule. As you can see, the magnitude of the resultant is nearly equal with that of the force F 3.

This geometrical solution is helpful because we know what results we should expect from the analytical solution. As expected, the analytic solution forces projection give the same results as the geometric solution polygon rule.

Example 2. For two-dimensional problems, we can write down the general equations to calculate the vertical and horizontal force components as:. Example 3. Observation : If the calculation is done on hand-held calculator of a software application, the argument of the cos function must be given in radians, for example:.

## What is the Resultant Force and How to Find it (with Examples)

Observation : If the calculation is done on hand-held calculator of a software application, the argument of the sin function must be given in radians, for example:.Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details.

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**Find F_1 sp that the resultant force is 450 along the u axis**

Electrical Engineering. Mechanical Engineering. Advanced Math. Advanced Physics.Hot Threads. Featured Threads. Log in Register. Search titles only. Search Advanced searchâ€¦. Log in. Contact us. Close Menu. JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Force Required to be a minimum. Thread starter Emilio Start date Feb 2, Homework Statement If the resultant force acting on the bracket is required to be a minimum, determine the magnitude of F1.

Last edited: Feb 2, NascentOxygen Staff Emeritus. Science Advisor. Emilio said:. NascentOxygen said:. Something important missing here? I'm not sure what you mean, am I missing a step or did I leave something out? There's a degree symbol?

The phi isn't showing up on my screen, it's just a blank space. Your mistake is in equating the sum of the components to zero. That would certainly be ideal, but with the angle fixed all you can aim for is a minimum, not zero. What does it mean to find a minimum? A minimum force that would keep it in equilibrium? The smallest possible resultant force?

The resultant sum of those 3 external forces is to be its smallest possible value.

Do I set up a limit as F x approaches 0? Log in or register to reply now!

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