Question

The greatest and the least resultant of two forces acting on a point are 29 Kgf and 5kgf. If each force is increased by 3kgf find the resultant of the new forces acting at an angle of 90degree with each other

Answer 1

Greatest when both are in same direction. Fmax = F1 + F2 =29 Kgf
Least when both are in opposite direction. F min=F1 -F2 =5 Kgf

So F1=17 and F2=12

Both increased So F1=20 , F2=15

Resultant force = ( 20*20 + 15*15)^1/2 = 25Kgf

Answer 2

Answer:

25kgf is the resultant of the new forces .

Explanation:

Given , the greatest and the least resultant of two forces acting on a point are 29kgf and 5kgh .

Let $F_1 and \ F_2$ be the two force .

Therefore , from the question the greatest resultant of two forces is 29kgf

⇒$F_1 + F_2$ = 29 kgf  .........(i)

And the least resultant of two force is 5kgf

⇒$F_1 - F_ 2$ = 5kgf .........(ii)

On adding (i) and (ii) we get ,

$(F_1+F_2) + (F_1 -F_2)$ = 29 + 5 = 34 kgf

⇒$2F_1$ = 34 ⇒$F_1 = \frac{34}{2}$ = 17 kgf

Now ,put the value of $F_1 = 17kgf$ in any one of the equation we get ,

17 - $F_2$ = 5

⇒$F_2$ = 17 - 5 =  12kgf.

According to the question each force is increase by 3kgf

So $F_1$ = 17 + 3 = 20 kgf and $F_2$ = 12 + 3 = 15 kgf

Therefore , the resultant of new force is ;

R = $\sqrt{F_1 ^2 + F_2^2 + 2F_1F_2cos\theta }$

⇒R = $\sqrt{20^2 + 15^2 + 2(20)(15)cos90}$  

[  Given , angle is  90° and cos 90 = 1 ]

⇒R = $\sqrt{400 + 225 + 0 } = \sqrt{625}$ = 25 kgf .

Hence , the resultant of the new forces is 25 kgf .

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