In the figure below, a spider is resting after starting to spin its web. The gravitational force on the spider is 0.167 N on the junction of the three strands of silk. The junction is supported by different tension forces in the two strands above it so that the resultant force on the junction is zero. The two sloping strands are perpendicular, and we have chosen the x and y directions to be along them. The tension Tx is 0.133 N.
To find the tension Ty in the other strand, we can utilize the concept of vector components. The given information states that the resultant force on the junction is zero, which means the vertical component of the tension forces should add up to counterbalance the gravitational force acting downwards.
To begin, we need to identify the different force vectors involved. We have the tension force Tx acting along the x-direction, the tension force Ty acting along the y-direction, and the gravitational force acting downwards.
Since the two sloping strands are perpendicular, the vertical component of the tension force Tx will cancel out with the vertical component of the gravitational force.
Let's start by determining the vertical component of Tx. We can do this using trigonometry. Since the two sloping strands are perpendicular, we can use the sine function to find the vertical component:
vertical component of Tx = Tx * sin(90°) = Tx
The vertical component of Ty will then balance out the vertical component of the gravitational force. Therefore, we have:
Ty + vertical component of Tx = gravitational force
Substituting the given values into the equation:
Ty + 0.133 N = 0.167 N
Now, we can solve for Ty:
Ty = 0.167 N - 0.133 N
Ty = 0.034 N
Therefore, the tension in the other strand Ty is 0.034 N.