Find the tension T2 of the box hanging from the rope if 1 = 25°, 2 = 65°, T1 = 60.58 newtons, and W = 143.4 newtons.
95.6 Newtons
To find the tension T2 of the box hanging from the rope, we can first apply the concept of equilibrium.
The tension T1 is acting at an angle of 1 = 25° with the vertical, and the weight W (force due to gravity) is acting vertically downwards.
We can use the concept of resolving forces into vertical and horizontal components. Let's denote the vertical component as T1v and the horizontal component as T1h.
Using trigonometry, we can calculate T1v and T1h as follows:
T1v = T1 * cos(1)
T1h = T1 * sin(1)
Now, let's consider the box hanging from the rope. The tension T2 is acting at an angle of 2 = 65° with the vertical. Similar to T1, we can calculate the vertical component (T2v) and horizontal component (T2h) of T2:
T2v = T2 * cos(2)
T2h = T2 * sin(2)
Since the box is in equilibrium, the sum of the vertical components of T1 and T2 must balance out the weight W:
T1v + T2v = W
Substituting the values we know:
T1 * cos(1) + T2 * cos(2) = W
Plugging in the given values of T1, 1, W and 2, we can solve for T2:
60.58 * cos(25°) + T2 * cos(65°) = 143.4
Now, we need to find T2 by rearranging the equation:
T2 * cos(65°) = 143.4 - 60.58 * cos(25°)
T2 = (143.4 - 60.58 * cos(25°)) / cos(65°)
By substituting the values and evaluating, T2 can be calculated.