FOR MATH. & PHYSICES EXPERTS ,How to find the max angle betn. the resultant of 2 forces & a force of them ?

1:

Draw a horizontal arrow of length F1. At the end of F1, draw a circle of radius F2. Every resultant force is a line connecting the start of F1 to a point on the circle.

The resultant with the maximum angle is the one that lies tangent to the circle and thus perpendicular to the radius of length F2. Thus, the force triangle that maximizes the angle between F1 and the resultant is a right triangle with hypotenuse F1 and leg F2 opposite the desired angle. Thus, we may state that for the maximum angle A between F1 and the resultant,

sin(A) = F2/F1

A = arcsin(F2/F1)

The necessary angle between F1 and F2 is A + 90 = 180 - arccos(F2/F1) = arccos(-F2/F1).

Diagram: http://flic.kr/p/dCX8Bk

2: the maximum angle is found by placing the two arrows in opposition. Since the resultant lies opposite F2, the angle between F2 and the resultant is 180˚.

Tarek Mounir Hi!

FOR MATH. & PHYSICES EXPERTS ,How to find the max angle betn. the resultant of 2 forces & a force of them ?

Given 2 forces F1 & F2 , where F1 > F2 , find the measure of the angle betn. F1 & F2 to :-

1) Maximise the measure of the angle betn. the resultant & F1 .

2) Maximise the measure of the angle betn. the resultant & F2 .

PLZ. prove your answer & show your steps .

The best answer will be chosen . THANKS IN ADVANCE .

Usually in actual problem in Physic like this the F1 & F2 is applied to the load W

Diagram : http://www.flickr.com/photos/27678773@N06/82984655...

W is the mass to be move by two FORCES F1 & F2.

F1 whose angle Ω is made between Line of Motion & its Force Direction.

F2 whose angle φ is made between Line of Motion & its Force Direction.

To find the Resultant Force of the two Forces [F1 & F2].

F2 will be transferred to the tip of F2 (dotted line)

1) Maximise the measure of the angle betn. the resultant R & F1

Let α be the angle Between Resultant Force to F1

Cosine Law

Cos α = [F1² + R² - F2²] / 2R F1

2) Maximise the measure of the angle betn. the resultant & F2 .

Let ß be the angle Between Resultant Force to F2

Cos ß = [F2² + R² - F1²] / 2R F2

Resultant Angle = Angle Ω – Angle α

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Lim♥E

Draw a 7.0 inch final prognosis from element "O". call the top element "Q" Open a compass10.5 inches and draw an arc with " O" as a midsection. Open the compass to eight.5 inches and draw an acr from the element "Q" because of the fact the midsection, this might intersect the different acr call the intersecting element of the arc as "R" connect "O", "R", and "Q" so as. this is your rigidity trangle. make larger the line "O - Q" to any length call the top poit of this line "P". attitude between "Q-P" and "Q-R" is the attitude between the two forces 80 5 lbs and 70 lbs. in basic terms for exciting complete the parellellogram and degree each and every element for accuracy (do no longer do it interior the examination if there is not any time left). Baseon the diagram you may verify all utilising trig fomula. this way you have batter be attentive to-how of the trignometri additionally.