The resultant of two forces,one is double in magnitude than the other,is perpendicular to smaller force.What is the angle between the two forces?
sinα =F₁/F₂=0.5
α= 30⁰,
the angle between the two forces
= 90⁰+30⁰=120⁰
To find the angle between the two forces, let's define the forces as follows:
Let the magnitude of the smaller force be F.
Since the larger force is double in magnitude, its magnitude would be 2F.
Given that the resultant of the two forces is perpendicular to the smaller force, we can conclude that the forces are acting at right angles to each other, making them orthogonal.
In a right-angled triangle, the angle between the two sides can be found using trigonometric functions. In this case, we can use the inverse tangent function (arctan) to find the angle.
So, the angle between the two forces can be calculated using the formula:
angle = arctan(opposite/adjacent)
In this case, the smaller force is the opposite side and the larger force is the adjacent side. Therefore, we have:
angle = arctan(F/2F)
Simplifying the expression, we get:
angle = arctan(1/2)
Using a calculator or mathematical software, we can find that the value of arctan(1/2) is approximately 26.57 degrees.
Therefore, the angle between the two forces is approximately 26.57 degrees.