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Four forces of magnitudes 1OON; 1SON 2OON,and 35ON are applied to an object as Find the magnitude of the fifth force, labeled F shown: that will produce diagram - a...

Question

Four forces of magnitudes 1OON; 1SON 2OON,and 35ON are applied to an object as Find the magnitude of the fifth force, labeled F shown: that will produce diagram - above. equilibrium in the force150 NZ0QN350 N100 NOa) F = 200 NC)6) F = 450 NOc F = 150 NFd) F ? 350 N

Four forces of magnitudes 1OON; 1SON 2OON,and 35ON are applied to an object as Find the magnitude of the fifth force, labeled F shown: that will produce diagram - above. equilibrium in the force 150 N Z0QN 350 N 100 N Oa) F = 200 N C)6) F = 450 N Oc F = 150 N Fd) F ? 350 N



Answers

Resultant Force Three forces with magnitudes of 400 newtons, 280 newtons, and 350 newtons act on an object at angles of $-30^{\circ}, 45^{\circ},$ and $135^{\circ},$ respectively, with the positive $x$ -axis. Find the direction and magnitude of the resultant force.

So in this case, we want to figure out the the result of a couple of vectors in three D and find the magnitude and direction of results. So of these two vectors, so one vector, it's called P. It has a magnitude of 300 Newton's, and it has an angle. It makes an angle of 30 degrees with the Oh, wait a minute labeled draw. Uh, yeah, this should be This is Q This is he. Okay, So cute, too has a magnitude of four hundreds, and it makes an angle or 50 degrees with the X y x z plane. So the y component we need to take an angle of 50 sign of 50 degrees and then for the x component way, Take way projected with co sign of 50 degrees in the XY plane and then co sign of 20 degrees under the X axis and sign up 20 degrees on the Y axis. And in this case, it is, um, it is in the negative direction, so we need a negative sign here. So one thing you can actually do if if you if you take some all of these things squared, you're gonna get one because this is a unit factor, it just gives the direction. And so P has a magnitude of 300 Newtons and it makes an angle of 30 degrees with the X y plane. So the Y component or the X Z plane, So the Y component is sign of 30 p time sign of 30 degrees. We project into the XY plane with co sign of 30 on. Then it has a negative X component, so negative coastline 30 and then it makes an angle of 15 degrees with the Z axis. So we have signed a 15 to get the X component and co sign of 15 to get the Z component. So then we just plug in all the values in here on again. I've I've written it in this kind of a rain notation, which means that we just some of the components and what we get is 174 Newtons in the X Direction 400 um, 56 Newton's in the Y direction and 163 Newton's in the Z direction. Find the magnitude we just take squares. Take the square root of the sum of the squares and we get 515 Newton's. And then again, to get these angles, we can just take the universe co sign of the components who was divided by the magnitude. And so we had the universe co sign of 174 divided by 515 on. That would give us 70.2 degrees, so this defector makes an angle 70.2 degrees with the X axis on 27.6 degrees with the Y axis and 71.5 degrees with Z axis.

To find the resultant force and problem 92. I need to find the components of each force and then add them together. They have forced p enforce que he's X component is gonna be in the negative X direction we take the result in force of P A. Multiply at times the co sign of 30 degrees to get it in the XY plane and then times a sign of 15 degrees to get in the X direction. And we end up with 89.7, Newton's negative 89.7. And for the y component, we have the 400 Newtons times the sign of 30 degrees, and it will already be in the Y direction that comes out to 200 Newtons for the Z direction. We're also going toe move it to the XZ plane with the coastline of 30 degrees and then multiplied by the co sign of 15 degrees. To get it in the Z direction, we get that that component of the force is 335 Newtons. Now, when you do the same thing for Q, it's the X component for Q is going to be equal to key was a result in Force 300 Nunes Times, a coastline of 50 degrees to get it in the XY plane and then times the co sign of 20 degrees. To get in the X direction, you get 181 Newtons for the X component of Q. The y component is going to be a little simpler again. We just have to multiply it by the sign of 50 degrees to be along that Why access Get 230 Newtons for the Y component Z component is in the negative z direction, and we're going to multiply the force times the co sign of 50 to get in the XY plane and then the sign of 20 degrees to get it along the Z axis that comes out to negative 66.0 Newtons. Now the resultant force of these two forces is going to be equal to the X components. Some together in the eye direction I component and for J will some the why and then we'll do the same for the Z components in the K direction. Forget that the result in force is equal to you. 91.3 Newtons for the I component post 430 Newtons for the J component and 269 Newtons for the K component. Now, to find the magnitude, we'll take the square root of the some of each component squared. We get that result in forces 550 Newtons. Now we need to find the angles each component of the angle that this resultant forces acting at do that using the equation that the co sign of the X component angle is equal to x amount of the force over the result in force. And we just solved for both the X component and the resultant force so we can solve for data in the X direction. We get it 79.8 degrees. We can use the same formula for the Y direction. You can plug in the Y component over the resultant force we found. We get the data in the Y direction as 33.4 degrees and lastly we have the Z component of the angle, which is going to be equal to 58

Advance. This is the problem based on additional factors. Here it is given to forces having the magnitude 13 Newton and 17 Newton are acting and a tangle 45 with positive excesses on one country degree with positive X success. As soon in the figure we're toe find the resultant off Afghan, plus a magnitude as Bella's direction. So Afghan factor can be written in components. For Mitch, you have to resolve this factor into its components of everyone cause 45 kept plus F one signed 45 Jacob Substitute develop Everyone is 30 cost 45 years burn upon roto I kept plus 30 into Bon upon to Jacob. So it is to be 15 road to I Care plus 15 roots. Jacob Newton. Similarly, I have to force to be dissolved into its company. Uh, it will be seven minus 70. Sign up 30 icap Well, so it is to be minus 35 Cap plus 35 a road trip. Jacob Newton so rejected. Forced off a one plus a new Cabinet. Allies 15 route toe I Cab has 15 route to Jacob plus minus 35. I kept less. 35. Route three J cap so it can be written as 15 route to minus 35 camp because 15 route to plus 35 four or three. Jacob. So you will get minus 30.79 I kept, plus 81.76 Jacob Newton. Now we have toe fire it the magnitude and direction off it magnitude off. It would be rude. Off minus 13 179 Holy Squared it was 81.764 is 12 on solving it. It's a magnitude ability 44.55 noted on the direction had probably 10 in worse off by component upon. So it is around. It was 60.2 kids protective X axis. Yeah, that's all. Thanks for

So we want to find the magnitude and direction of the resultant wind. Two forces air acting on an object. One of our forces is 30. Newton's forming an angle of 45 degrees with the X axis. The other force is 70. Newton's forming an angle of 120 degrees with the X axis. So what we're gonna do is use trigonometry to help us find the components of each factor. And then we can easily do vector addition to get the components of our resultant vector. So to start the components of our first vector F one first, we want to remind ourselves that the horizontal component is going to be our Tshosane data. Where are is the magnitude of our vector and why is r sine data? So our first vector F one is going to have components of 30 consigned 45 degrees and 30 time sign 45 degrees. Simplifying that cosign 45 is one over square root too. So we have 30 over square to, and same thing with signed 40 fives else's one over square it too. So our components oh, are identical. So dirty over to 30 over around two. Our second vector has components 70 co zone 1 20 and 70 Sign 1 20 So coastline of 120 degrees is negative. Half, I said we had 70 times negative half and then sign of 120 degrees is square in 3/2. So let's simplify that to get negative. 35 and 35. Grab three. Those are components of F. Teoh, our second director over here. So now we can just add those components together and the corresponding opponents. So 30 over rad too. Plus negative 35 or minus 35. That's the horizontal component of our results, Inspector. And the vertical component is 30 over rad too, plus 35 grabbed three. If we get the decimal values using our calculator, that would be negative. 13 point 787 and 81 0.83 fire. You could see that a result in vector would be in the second quadrant, Probably something like that. So now we need to find the magnitude of our results in factor. So we need to take the square root of the sons of the squares of the components. So in our calculator, I'm going to do. Negative. 13.78 seven squared plus 81 point feet +35 squared. And that's going to give us 82.9 80. So that's the magnitude of our resulted director of one plus two. Now we need to figure out the direction. What is this angle measure? From the X axis to the resultant, we can use trigonometry to help us again. We can use sign in verse, co sign inversion tangent. Inverse. It doesn't really matter. I'm gonna use tangent. Inverse. We know that Tangin inverse of the vertical component over the horizontal component is going to give us our angle measure. So we're gonna do tan in verse, uh, 81.835 over negative 13.787 And that's going to give us negative et point for 37 breeds. Make sure you're in degree load on your calculator. Unless the question is specifically asking you for radiance. Now, the negative 80.437 degrees is not in Quadrant two. That's in quadrant four. So we need to think about this. We need quadrant to angle measure so we can take the absolute value of negative. 80.437 And that gives us our reference angle. So this angle right here is negative. 80. Excuse me. 80.437 So, what we're going to do to get the angle measure that we want use? Subtract 80.437 from 180 and that will give us 99 0.563 degrees. That's the direction. So are resultant. So remember, we have two parts to answer the direction and the magnitude of the result.


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