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Resolution and Composition of Forces – Problem 1 – Engineering Mechanics

September 10, 2019


hello students today we will solve some problems on resolution and composition of forces let me take the first question and next we are going to read the question okay find the magnitude and direction of resultant of the following system of forces first posed 4 Newton due north second 3 Newton acting Northwest towards the point third one point 5 Newton acting due east fourth one Newton 30 degree west of south away from the point and last five Newton acting 60 degree north of West away from the point it means in this question they have not given the diagram but they have given you some instructions here with the directions of forces and the value of forces and they are telling you to find magnitude and direction of resultant here we have to calculate what is the resultant its value and we have to also locate the resultant so we will start with this problem first I will write the data for this in this problem whatever data is given I will draw it in the form of a diagram first let me see here for Newton force is do not for Newton forces do not so let me draw the diagram for this whatever data is given we will convert it into a diagram in this case I will mark the directions since here they have given you the directions in the form of north south east and west so instead of writing x and y axis I will write the directions here I will be marking let us see the first pose for Newton do not it means the force will be here it will be acting in the north direction so here I have four Newton force second three Newton acting north west towards the point three Newton is acting not waste what is the meaning of North West here I have north here is West so in between them that is the angle between north and west is 90 degrees so you have to take exactly half of that means 45 degree at 45 degree we have a force and the value of forces three Newton and it is acting towards the point towards the point means it is acting you can say towards the origin okay and the value is three Newton inclination is 45 degree with horizontal as well as vertical then one point 5 Newton acting due east 1 point 5 Newton acting due east then 1 Newton 30 degree west of south away from the point 1 Newton half or 30 degree best of South here I have south this is east of South this is west of South so 30 degree to the west of south yes it is 30 degree to the west of South means it will be somewhere here ok and what is it it is away from the point away from the point the value of the forces 1 Newton 1 Newton it is at 30 degree 30 degree to the west of South then 5 Newton acting 60 degree north of West away from the point the direction is north of waste here I have not okay here I have west and south so not off West will be on this side north of West and inclination is 60 degree so it will be like this value of force it is 5 Newton acting 60-degree north of waist away from the point it is acting away from the point value is 5 Newton so this is the diagram which we have from the data which they have given here I have to calculate the value of resultant that is the magnitude of resultant and then I have to calculate the inclination means location of resultant so now we will solve this problem how to solve this problem first of all you have to convert all the forces which they have given even if they are inclined incline forces you have to convert all the inclined forces into horizontal and vertical components here I have horizontal component which is 1 point 5 Newton it will remain as it is 4 newton is vertical that will remain as it is now if we talk about this 5 Newton it is inclined at 60 degree to horizontal so this 5 Newton will be resolved I am going to resolve this 5 Newton force and if I am resolving I will get my horizontal component as it will be force which is 5 angle is 60 degree so I have to write down cos 60 degree vertical component that will be 5 sine 60 degree after this here I have 3 Newton force at 45 degree but the thing is it is acting towards the point so here I will be marking its horizontal component and its vertical component since it is inclined at 45 degree with the horizontal value is 3 Newton so I will write down 3 cos 45 and for this vertical component I am just writing it as 3 sine 45 degree then 30 degree at 30 degree you have 1 Newton force inclination is with respect to vertical so this horizontal component will be 1 sine 30 degree vertical component will be 1 cos 30 degree with this much data where we have you can say so resolve the components into horizontal and vertical form now we can easily start with the problem that is the calculation of resultant I hope y’all have understood this so I will write the solution for this problem I can write down since the sum of all horizontal forces since the sum of all is given by summation of fx and here the convention is positive forces that is towards right the forces should be taken as positive forces towards left should be taken as negative now we will write summation of f X so therefore summation of FX is equal to here I have 1 point 5 Newton towards right positive then 5 cos 60 towards left negative then three cos 45 towards right positive one sign 30 towards left negative so here I have all the forces which are horizontal forces therefore if I calculate the value my summation of FX comes out to be here I have the answer which I have already calculated it is 0.62 one Newton answer is positive therefore you have to show it towards the right side I hope you are getting this then I will write also the sum of all vertical forces some of all vertical forces are given one summation of FY is equal to upward forces are taken as positive downward forces they are taken as negative so therefore I can say summation of effects or here I have FY that will be equal to here I have 4 Newton force which is acting upwards so I will take it as positive 5 sine 60 that is upward so positive three sine 45 downwards so negative 1 cos 30 downwards so negative so in totality here I have 1 2 3 & 4 4 vertical forces so therefore if I calculate all the values I will get my summation of FY is equal to my answer is 5 point 3 4 Newton since it is positive it means it is a Thing upward direction next after this I can calculate the resultant I can easily get the resultant we know the formula of resultant I can write it down now since resultant is given by capital R is equal to square root of summation F X whole square plus summation F Y whole square therefore R is equal to square root of summation F X the answer which I have got of summation F X is 0.62 1 Newton so it is 0.62 1 whole square plus summation F Y is 5 point 3 4 5 point 3 4 whole square therefore my answer of resultant if I calculate this entire term my answer comes out to be 5 point 3 8 Newton my answer comes out to be 5 point 3 8 Newton that this I have got my first answer after getting the value of resultant now we will find the location of the segment I can write down since location of resultant is given my location of resultant is given by theta is equal to tan inverse summation FY upon summation F X we will highlight this therefore theta is equal to tan inverse of summation FY the value was one 5.34 for summation F X 0.62 one if I calculate theta my answer will be eighty three point three seventh degree that is with respect to horizontal so this is my second answer after getting resultant and its location we can easily show the resultant on a diagram let me represent it the directions were given in the form of north-south-east-west inflammation is 83.37 and if you look at this question here when we had solved summation F X was positive submission fy was positive so summation F X is positive it means it is along horizontal positive side summation F Y positive means it is along the vertical side so it means resultant will be in the first quadrant and its inclination is 83 point three seven degrees thirty three point three seven degree value of this resident it was five point three eight Newton so in this problem we have calculated the resultant and even shown its location so this complete the solution to the problem since location of resultant is given by theta is equal to tan inverse summation FY upon summation F X therefore theta is equal to tan inverse summation F I FY was five point three four summation F X zero point six two one if we calculate this value theta will be eighty three point three seven degree with respect to horizontal so this is my second answer next we can even locate the resultant by drawing the axis in this problem they have given us axis in the form of north south east and west directions so we can mark north south east and west and then locate the resultant inclination is eighty three point three seven degree so Teta value I have found out so I can show the inclination of resultant adds eighty three point three seven degree and the value of resultant is five point three eight Newton and with this we have completed the first problem now let us take the next problem

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