Question

Five coplanar forces are acting on a particle of mass
m such that the angle between any two adjacent
forces is 72°. Four forces are of magnitude F, and
one of F2. The resulting acceleration of particle is​

Answer 1

Answer:

$a = \frac{F_2 - F}{m}$

Explanation:

As we know that all the forces are co-planar and lying at equal angle with each other

So here we know that

$\vec F_1 + \vec F_2 + \vec F_3 + \vec F_4 + \vec F_5 = F_{net}$

if all five forces are of same magnitude and lying at equal angle with each other then the resultant must be zero

so we have

$\vec F_1 + \vec F_2 + \vec F_3 + \vec F_4 + \vec F_5 = 0$

so we can say

$\vec F_1 + \vec F_2 + \vec F_3 + \vec F_4 = -\vec F_5$

so sum of 4 co-planar equal forces must be equal to the 5th force in opposite direction

here we can say that

$\vec F + \vec F + \vec F + \vec F = - \vec F$

now the resultant of given forces is

$F_{net} = F_2 - F$

now the acceleration is given by Newton's 2nd law

$a = \frac{F_{net}}{m}$

$a = \frac{F_2 - F}{m}$

#Learn

Topic : Vector addition and newton's Law

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