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.

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.

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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:.

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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:.Questions are typically answered within 1 hour.

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

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the resultant force is directed along the positive y axis and has a

Solution Parallelogram Law. The parallelogram law of addition is shown in Fig. Applying Law of cosines by referring to Fig. Resolve the force F1 into components acting along the u and v axes and determine the magnitudes of the components. Applying the sines law by referring to Fig.

Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components.

the resultant force is directed along the positive y axis and has a

Applying the sines law of referring to Fig. The parallelogram law of addition and the triangular rule are shown in Figs. Applying the law of consines to Fig. If the magnitude of the resultant force is to be N, directed along the positive y axis, determine the magnitude of force F and its direction u. Applying the law of cosines to Fig. Solution The parallelogram law of addition and the triangular rule are shown in Figs. Applying the law of sines to Fig.

If the resultant force is required to act along the positive u axis and have a magnitude of 5 kN, determine the required magnitude of FB and its direction u. Resolve F1 into components along the u and v axes and determine the magnitudes of these components. Resolve F2 into components along the u and v axes and determine the magnitudes of these components.

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The device is used for surgical replacement of the knee joint. If the tension in the cable is N, determine the magnitude and direction of the resultant force acting on the pulley. This angle defines the same angle T of line AB on the tailboard block.

The truck is to be towed using two ropes. Determine the magnitude of forces FA and FB acting on each rope in order to develop a resultant force of N directed along the positive x axis. Solution Parallelogram Law: The parallelogram law of addition is shown in Fig. Trigonometry: Using law of sines [Fig.

The plate is subjected to the two forces at A and B as shown. Determine the angle of u for connecting member A to the plate so that the resultant force of FA and FB is directed horizontally to the right. Also, what is the magnitude of the resultant force? Two forces act on the screw eye. Applying law of cosines to Fig. Two forces F1 and F2 act on the screw eye.

Determine the magnitude and direction of the resultant force, FR measured counterclockwise from the positive x axis.It basically says that you need to find an angle so that you can get away with the smallest possible value of F2. If you try angles other than 90 degrees you will discover that F2 must be greater than this value.

Minimum magnitude at other than along the x axis, so in the diagram, F2 would need to be a force equal to F1, and at the same angle 60 degrees from the x axis. Neither the force F2 nor the angle were given, and only if either one was a given, could you answer otherwise.

The y component of F1 and the y component of F2 would need to be equal here. So both x components must be equal also. After you found this, you are down to only one unknown. Trending News. Hailey Bieber endorses Biden — while dad backs Trump. Ex-Obama adviser: Covid infections 'going to go up'.

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Wallace grills Lara Trump for breaking debate rule. North Korea unveils new weapons at military parade. I'm studying statics, and this has come up in more than one question. For example: It is required that the resultant force acting on the eyebolt in Fig 2.

Answer Save. Andrew Smith Lv 7. This is the smallest possible value consistent with the question. Technobuff Lv 7. Very simple Allison Trochie. Still have questions? Get your answers by asking now.Ask your question! Help us make our solutions better Rate this solution on a scale of below We want to correct this solution. Tell us more Hide this section if you want to rate later. Questions Courses. Nov 06 PM. Mohammedali A answered on September 11, Do you need an answer to a question different from the above?

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Find the resultant force with the minimum F_b

Related Questions. If the magnitude of the resultant force is to be Ndirected along the positive y axis, determin. If the magnitude of the resultant force is to be Ndirected along the positive y axis, determine the magnitude of force F. If the magnitude of the resultant force is to be Ndirected along the positive y axis, determine the force F If the magnitude of the resultant force is to be N, directed along the positive y axis, deter If the magnitude of the resultant force is to be N, directed along the positive y axis, determine the magnitude of force F and its direction theta.Windows Mac Linux Android iOS Reviews Info Contact DMCA Request Submit Software Terms of Use Privacy Policy Sitemap Latest reviews UFRaw Amazon for Tablets Virtual Dentist Surgery Free VPN -Hotspot Shield Basic JPEGView - Image Viewer and Editor Other projects Backup Software PDF Printer Free PDF converter Free Backup software Free Burning Software Quotes on Enquoted.

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the resultant force is directed along the positive y axis and has a

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If Φ = 45°, F1 = 5kN, and the resultant

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