# A picture hangs on the wall suspended by two strings, with è = 61°. The tension in string 1 is 1.8 N.

è is connected to string 1, and 32° is connected to string 2.

(a) Is the tension in string 1 greater than, less than, or equal to the tension in string 2?

greater than

less than

equal to

.

Explain.

(b) Verify your answer to part (a) by calculating the tension in string 2. N

(c) What is the weight of the picture?

N

## (a) To determine whether the tension in string 1 is greater than, less than, or equal to the tension in string 2, we can consider the forces acting on the picture. Since the picture is at rest, the net force acting on it must be zero. This means that the vertical component of the forces must cancel out.

Let's break down the forces acting on the picture. The weight of the picture is acting vertically downward. We can represent this force as the force due to gravity, which is equal to the weight of the picture.

The tension in string 1 has a vertical component and a horizontal component. The vertical component of tension 1 opposes the weight of the picture, trying to lift it. The horizontal component of tension 1 has no effect on the vertical forces.

Similarly, the tension in string 2 also has a vertical and horizontal component. The vertical component of tension 2 also opposes the weight of the picture, trying to lift it.

Since both tension 1 and tension 2 are opposing the weight of the picture, the total upward force provided by the tensions should be greater than the downward force of the picture's weight.

Therefore, the tension in string 1 is greater than the tension in string 2.

(b) To verify our answer, let's calculate the tension in string 2. To do this, we can use trigonometry.

Since we know that tension 1 is 1.8 N and the angle between tension 1 and the vertical is 61°, we can use trigonometric functions to find the vertical component of tension 1.

Vertical component of tension 1 = Tension 1 * sin(angle)

Vertical component of tension 1 = 1.8 N * sin(61°)

Now, we can use the vertical component of tension 1 to find the tension in string 2. Since the vertical component of tension 1 should be equal to the vertical component of tension 2, we have:

Vertical component of tension 1 = Vertical component of tension 2

1.8 N * sin(61°) = Tension 2 * sin(32°)

Solving for Tension 2:

Tension 2 = (1.8 N * sin(61°)) / sin(32°)

Calculating this value will give us the tension in string 2.

(c) To calculate the weight of the picture, we can use the formula:

Weight = mass * gravity

However, since the mass of the picture is not given, we need some additional information to determine its weight accurately.