Force 1= 65 pounds , Force 2=90 pounds
find the angle between the forces?
magnitude of the resultant force= 70lbs
use law of cosines.
70^2 = 65^2 + 90^2 - 2(65)(90)cosθ
thank you
To find the angle between two forces, we can use the concept of vector addition and the law of cosines.
First, let's draw a diagram to visualize the problem:
<----- Force 1 (65 lbs)
|
| Resultant Force (70 lbs)
|
-----> Force 2 (90 lbs)
Now, we need to find the angle between Force 1 and Force 2.
Step 1: Find the magnitude of the vector sum (resultant) of Force 1 and Force 2.
The magnitude of the resultant force is given as 70 lbs.
Step 2: Apply the law of cosines to find the angle between the forces.
The law of cosines states that for a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:
c^2 = a^2 + b^2 - 2*a*b*cos(C)
In this case, let a = 65 lbs, b = 90 lbs, and c = 70 lbs. We are interested in finding angle C.
Plugging these values into the equation, we have:
70^2 = 65^2 + 90^2 - 2*65*90*cos(C)
Simplifying the equation, we get:
4900 = 4225 + 8100 - 11700*cos(C)
Rearranging the equation, we have:
-7400 = -11700*cos(C)
Dividing both sides of the equation by -11700, we get:
cos(C) = -7400/-11700
cos(C) = 0.632
Now we need to find the inverse cosine (cos^-1) of 0.632 to get the angle C.
Using a calculator or a mathematical software, we find:
C = cos^-1(0.632) = 50.65 degrees (approximately)
Therefore, the angle between the forces, Force 1 and Force 2, is approximately 50.65 degrees.