Pulling the string on a bow back with a force of 28.7 lb, an archer prepares to shoot an arrow. If the archer pulls in the center of the string, and the angle between the two halves is 138*, what is the tension in the string?
2 T cos (138/2)= 28.7
To find the tension in the string, we can use the concept of vector addition.
First, we need to split the force into two components. Since the force is being pulled in the center of the string, each half of the string experiences an equal force of 28.7 lb.
Next, we need to find the vertical component of the force. To do this, we can use trigonometric functions. The vertical component can be found by multiplying the force by the sine of half the angle between the two halves of the string:
Vertical component = Force * sin(angle / 2)
Here, the angle is given as 138 degrees, so the vertical component is:
Vertical component = 28.7 lb * sin(138 / 2)
After calculating this value, we get the vertical component of the force.
Finally, to find the tension in the string, we add the vertical component to the horizontal component (which is equal to the force):
Tension in the string = Horizontal component + Vertical component
By performing this vector addition, we can determine the tension in the string.