Five forces inclined at an angle of 72° to each other are acting on a particle of mass m placed at origin of coordinates. Four forces are of magnitude F1 and one F2. Find resulting acceleration of particle
Answers
Given:
Five forces inclined at an angle of 72° to each other are acting on a particle of mass m placed at origin of coordinates.
Four forces are of magnitude F1 and one F2.
To find:
Find resulting acceleration of particle.
Solution:
Consider the attached figure while going through the following steps.
We are given,
Five forces inclined at an angle of 72° to each other.
Four forces are of magnitude F1 and one F2.
The force acting at +x axis
F1 cos 72° + F2 + F1 sin 18° = 0.6F1 + F2
The force acting at -x axis
F1 sin 54° + F1 cos 36° = 1.6F1
The force acting at +y axis
F1 sin 72° + F1 cos 54° = 1.5F1
The force acting at -y axis
F1 cos 18° + F1 sin 36° = 1.5F1
The resultant force at y-axis is given by,
(1.5 F1) - (1.5 F1) = 0
The resultant force at x-axis is given by,
(0.6 F1 + F2) - (1.6F1) = F2 - F1
Therefore, the total resultant force is F2 - F1.
The acceleration is given by,
Acceleration = Force / Mass
a = (F2 - F1)/m
Therefore, the resulting acceleration of particle is (F2 - F1)/m
