Three forces act at point O. If it is known that the...

Three forces act at point O. If it is known that the y-component of the resultant R is -3.0 kN and that the z-component is 3.9 kN, determine F3, ?, and R. F3 z F2 = 4.8 kN ? O F1 = 5.9 kN x y Answers: F3 = kN ? = R = kN

Transcript

00:01 We're given here three forces act on a point o so we can write here three forces here we can write three forces that act on a point oh acting on a point oh if unknown that y component of the resultant is minus three k here by common result in r so we can write r y which is equal to we can write minus 3 kilo newton and the that j component of the j component is so we can write r to z which is equal to we can write here it is 3 .9 kilo home so we can write here by camera which will run for and let's determine the f3 theta and r so let's determine value of f3 theta and r so we want to find this and we are given here f1 and f2 so we are given f1 which is equal to 5 .9 5 .9 kilo newton we are given f2 which is equal to 4 .8 kilo newton and here we are given f3 also so now let's solve this question and find out the return of r.

01:07 So here we can write the cartesian form of f3 which is equal to we can write f3 by cost theta j garrat plus we can write f3, one level by sine theta k here we can write r which is equal to f1 plus f2 plus f3 and now here we just substitute value in this formula so you can write r which is equal to 5 .7 j karat 7 i karat minus f3 cost theta j karat plus you can write f3 sine theta k k karat now here f1 is 5 .9 and here we are given a 4 .8 here let's simplify and we can write here minus 4 .8 i .karrid here plus we can write jkarrate and into the bracket 5 .9 minus we can write f3 cost theta and plus we can write f3 multiplied by sine theta k correct so this is the value of the result now here i can write the y component here the ovi component of the result is minus 3 .5.

02:37 Minus 3 which is equal we can write here here we can write 5 .9 minus f3 cost data.

02:45 Now we just simply find we can write here so f3 cost theta which is equal to we can write here 8 .9 kilo home 9 kilo newton so this is the value of f3 or theta now we can write this this is z component so we can write here is z component is f3 sine theta so we can wait it's jr component f3 sign theta which is equal to the value here that is f3 sine theta that value is in the jr direction equal to answer is 3 .9 kilo newton so this is the value of f3 cost beta now let's find out the 10 theta so how to find this so we just taking a ratio so we can write 10 theta which is equal to we can write 10 theta which is equal to we can write here this is a sign theta here not cost theta right sign theta so we can write here 3 .9 divided by we can write here 8 .9 now we just simply find we can write here answer is so your theta which is equal we can write answer is right here answer is 23 .66 degree so this is the value of theta let's find out the value of f3 so how to find value of f3 so we can write f3 which is equal to we can write 3 .9 here we can write 3 .9 divided 3 .9 whatever we can write here sign 23 .6 degree.

04:13 Let find we can write your answer is 9 .71 kilo newton so this is the value of f3 here find out the general force so here we can write the regional force r which is equal to 4 .8 i.

04:27 Karate we are making right for minus 4 .8 i...

Question

Three forces act at point O. If it is known that the y-component of the resultant R is -3.0 kN and that the z-component is 3.9 kN, determine F3, ?, and R. F3 z F2 = 4.8 kN ? O F1 = 5.9 kN x y Answers: F3 = kN ? = R = kN

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