The ends of a rope are tied to two hooks on a ceiling. A set of books weighing 36.0 N is tied and hung on the rope so that the segments of the rope make angles of 35 degrees and 50 degrees respectively with the horizontal. Compute for the tension on each segment of the rope.

T1*Cos(180-35) + T2*Cos50 = -36*Cos270.

-0.819T1 + 0.643T2 = 0.
T1 = 0.785T2.

T1*sin(180-35) + T2*sin50 = -36*sin270.
0.574T1 + 0.766T2 = 36.
Replace T1 with 0.785T2:
0.574*0.785T2 + 0.766T2 = 36.
0.451T2 + 0.766T2 = 36.
1.22T2 = 36.
T2 = 29.6 N.

T1 = 0.785T2 = 0.785 * 29.6 = 23.2 N.

To compute for the tension on each segment of the rope, we will make use of the concept of equilibrium. In this case, we will consider the horizontal and vertical components of the tension.

Let's start by determining the horizontal components of the tension on each segment of the rope.

For the segment with an angle of 35 degrees with the horizontal, the horizontal component of the tension can be calculated using the formula:
T1_H = T1 * cos(35)

For the segment with an angle of 50 degrees with the horizontal, the horizontal component of the tension can be calculated using the formula:
T2_H = T2 * cos(50)

Next, let's determine the vertical components of the tension on each segment of the rope.

For the segment with an angle of 35 degrees with the horizontal, the vertical component of the tension can be calculated using the formula:
T1_V = T1 * sin(35)

For the segment with an angle of 50 degrees with the horizontal, the vertical component of the tension can be calculated using the formula:
T2_V = T2 * sin(50)

Since the system is in equilibrium, the sum of the vertical components of tension in each segment must equal the weight of the books (36.0 N). Thus, we can write the equation:

T1_V + T2_V = 36.0 N

Similarly, the sum of the horizontal components of tension must be zero. Thus, we can write the equation:

T1_H + T2_H = 0

We can now substitute the values for the horizontal and vertical components of tension into the equations above to solve for T1 and T2.

Let's start by substituting the formulas for the horizontal components:

T1 * cos(35) + T2 * cos(50) = 0

Next, substituting the formulas for the vertical components:

T1 * sin(35) + T2 * sin(50) = 36.0 N

Now, we have a system of two equations with two unknowns (T1 and T2). We can use algebraic methods (e.g., substitution or elimination) to solve for T1 and T2.