The resultant of two forces 12N and 5N is 13N. What is the angle between the two forces?
Answer Details
To find the angle between two forces, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the angle between them.
In this case, the two forces are the other two sides of the triangle, and the resultant force is the side whose length we know. Let's call the angle between the two forces θ.
Using the law of cosines, we have:
13^2 = 12^2 + 5^2 - 2(12)(5)cosθ
169 = 144 + 25 - 120cosθ
cosθ = (169-144-25)/(-2*12*5) = -1/8
Since cosine is negative, the angle θ must be in the second or third quadrant (where cosine is negative). To find the angle, we can take the inverse cosine (also known as arccosine) of -1/8:
θ = arccos(-1/8) ≈ 100.19 degrees
Therefore, the angle between the two forces is approximately 100.19 degrees. This is closest to the third option, which is 90 degrees.