The three cable forces act on the eyebolt as shown in...

The three cable forces act on the eyebolt as shown in (Figure 1). Part A Determine two possible magnitudes for P so that the resultant force has a magnitude of 950 lb. Express your answers in in pounds to three significant figures and separated by a comma. P = lb

Transcript

00:01 Hello students in the question it is given that three forces are acting on an eye bolt here for force f1 we need to find this angle phi so here we have tan phi it is equal to perpendicular that is 4 divided by base that is 3 so from here we get phi it is equal to tan inverse of 4 by 3 this comes out to be equal to 53 .13 degrees now here we have resolved these forces into horizontal and vertical components so we can write here horizontal component horizontal components summation fx this is equal to here we have f1 cos phi plus f2 cos 30 degree and we have another force here in this direction minus p here we can write summation fx it is equal to 1000 into cos 53 .13 degrees plus 400 into cos 30 degrees minus p here we get summation fx it is equal to 946 .4116 minus p now we have to calculate vertical forces here we have vertical component summation fy it is equal to here we have f1 sin phi minus f2 sin 30 degrees so here we get summation fy it is equal to 1000 sin 53 .13 degrees minus 400 sin 30 degrees this comes out to be equal to summation fy this is equal to 599 .9989 pound this is also in units of pound now we have resultant r it is equal to under root summation fx square plus summation fy square in the question we are given resultant it is equal to 950 pound let us substitute the values in this relation and we get 950 it is equal to under root 946 .4116 minus p whole square plus 599 .9989 square this is in under root or here squaring on both the sides we get 950 square this is equal to 946 .4116 minus p whole square plus 599 .9989 square so here we get 902500 this is equal to 895696 .92 plus p square minus 1892 .82 p plus here we have 359998 .68 so from here we get equation p square minus 1892 .82 p plus 353195 .6 this is equal to 0 now this is a quadratic equation of the form ax square plus bx plus c it is equal to 0 and we get root x it is equal to minus b plus minus under root p square minus 4ac divided by 2a here a b and c these are coefficients so here we get p it is equal to minus of minus 1892 .82 plus minus under root 1892 .82 square minus 4 into 353195 .6 this is an under root divided by 2 here this comes out to be equal to 1892 .82 plus minus 1473 .087 divided by 2 from here we get p it is equal to 1682 .95 pound and we have another value p it is equal to 209 .866 pound here we can approximate this as 1860 pound and this value as 210 pounds so here we have final answer that p it is equal to 1860 comma 210...

Question

The three cable forces act on the eyebolt as shown in (Figure 1). Part A Determine two possible magnitudes for P so that the resultant force has a magnitude of 950 lb. Express your answers in in pounds to three significant figures and separated by a comma. P = lb

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