An object with a weight of 150 N hangs from the ceiling as shown in the figure.

1) Find the tension in each string. q1 = 60 degree and q2 = 45 degree

1. -T1*Cos60 = -T2*Cos45.

T1 = -T2*Cos45/-Cos60 = 1.41T2.

T1*sin60 + T2*sin45 = -(-150).
0.866T1 + 0.707T2 = 150,
0.866*(1.41T2) + 0.707T2 = 150,
1.225T2 + 0.707T2 = 150,
1.93T2 = 150, T2 = 77.7 N.

T1 = 1.41 * 77.7 = 109.9 N.

To find the tension in each string, we can analyze the forces acting on the object.

Let's assume that the two strings (string 1 and string 2) are connected to the object at points A and B, respectively. The weight of the object acts vertically downward from point A. Since the object is in equilibrium, the sum of the vertical forces acting on it must be zero.

First, let's resolve the weight of the object into its vertical and horizontal components. The vertical component (W_vert) is given by:

W_vert = W * cos(q1)

where W is the weight of the object and q1 is the angle between the weight and the vertical axis (in this case, the ceiling).

Substituting the given values, we have:

W_vert = 150 N * cos(60°)
= 75 N

Now, let's consider the forces acting on the object in the vertical direction. There are two tension forces acting upward from points A and B. Let's denote the tensions in string 1 and string 2 as T1 and T2, respectively.

Since the object is in equilibrium, the net vertical force is zero:

T1 * cos(q1) + T2 * cos(q2) - W_vert = 0

Substituting the known values, we have:

T1 * cos(60°) + T2 * cos(45°) - 75 N = 0

This equation allows us to determine the relationship between T1 and T2.

To find the values of T1 and T2, we need one more equation. We can consider the horizontal forces acting on the object. There are two tension forces acting horizontally from points A and B, and they should balance each other out to keep the object in equilibrium.

Therefore, the horizontal component of T1 should be equal to the horizontal component of T2:

T1 * sin(q1) = T2 * sin(q2)

Substituting the given values, we have:

T1 * sin(60°) = T2 * sin(45°)

Now we have two equations:

1) T1 * cos(60°) + T2 * cos(45°) - 75 N = 0
2) T1 * sin(60°) = T2 * sin(45°)

To solve these equations simultaneously, we can use algebraic methods or trigonometric identities. Let's solve them using trigonometric identities.

From equation (2), we can write:

T1 = T2 * sin(45°) / sin(60°)

Substituting this value of T1 into equation (1), we get:

(T2 * sin(45°) / sin(60°)) * cos(60°) + T2 * cos(45°) - 75 N = 0

Simplifying this equation will give us the value of T2.

Once we have T2, we can substitute it back into equation (2) to find T1.