# Solving Chandelier Problem: T1, Sine/Cosine Confusion

• cameuth
In summary, the chandelier in the concert hall is attached to the ceiling by two cables that are attached near the walls due to intricate decorations on the ceiling. Cable 1 has tension T1 and makes an angle theta with the ceiling, while Cable 2 has tension T2 and makes an angle with the ceiling. To determine whether to use sine or cosine in the Newton's second law equation, draw a triangle with the tension in the cable and use trigonometry to find the horizontal and vertical components. In this case, since the angle is with the ceiling, you would use cosine for both the x and y directions.
cameuth
1. A chandelier with mass is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension and makes an angle of with the ceiling. Cable 2 has tension and makes an angle of with the ceiling.

3. I have a free body diagram, but I'm not sure whether or not T1 in the y direction should have a sine or cosine in the Newton's second law equation. actually, I'm not sure how to determine sine or cosine for anything going in a direction not directly along the x or y-axis in a Newton's second law problem. Can anybody help?

Whether you use sine or cosine depends on which angle you use (you could measure the angle that the string makes with the horizontal or with the vertical).

Draw a triangle with the tension in the cable to find its horizontal and vertical components. Label the angle that you know and then use trigonometry to determine whether you should use sine or cosine.

EDIT: Sorry, just saw that you specified the angle is with the ceiling. Still, draw a right angled triangle with the known angle and use trigonometry.

so, for the x direction it would be:
T1cos(theta)-T2cos(theta)?

Looks good to me; and that would be equal to zero, right?

[/b]

I can provide some guidance on how to solve this chandelier problem and address the confusion around the use of sine and cosine in Newton's second law equation.

First, it is important to understand that sine and cosine are trigonometric functions that relate the angles of a triangle to the lengths of its sides. In this chandelier problem, the angles and tensions of the cables are related to the weight and motion of the chandelier.

To determine whether sine or cosine should be used in the Newton's second law equation, we need to consider the direction of the forces acting on the chandelier. In this case, the forces are the tensions of the cables. When we draw a free body diagram, we can see that the tension in cable 1 is acting in the y-direction and the tension in cable 2 is acting in the x-direction.

Since we are interested in the forces in the y-direction, we should use the sine function to relate the angle to the tension (T1sinθ). Similarly, for the x-direction, we should use the cosine function (T2cosθ). This allows us to accurately calculate the net force acting on the chandelier in each direction.

It is important to note that the use of sine and cosine in Newton's second law equation is not limited to just the x and y-directions. They can also be used for any direction as long as we are considering the forces acting in that direction.

In summary, to solve this chandelier problem, we need to use the trigonometric functions of sine and cosine to relate the angles of the cables to the tensions in the Newton's second law equation. This will allow us to accurately calculate the net force acting on the chandelier and solve the problem.

## What is the "Chandelier Problem"?

The "Chandelier Problem" is a physics problem that involves calculating the tension of the wires holding a chandelier in place. It is often used as a practice problem for students learning about tension and forces in physics.

## What is T1 in the "Chandelier Problem"?

In the "Chandelier Problem", T1 refers to the tension in the top wire that is holding the chandelier up. It is an important variable in solving the problem and is typically denoted by T1 in equations.

## What is the difference between sine and cosine in the "Chandelier Problem"?

Sine and cosine are both trigonometric functions that are used in the "Chandelier Problem" to calculate angles and forces. Sine is the ratio of the opposite side of a right triangle to the hypotenuse, while cosine is the ratio of the adjacent side to the hypotenuse.

## How do I know which trigonometric function to use in the "Chandelier Problem"?

The trigonometric function to use in the "Chandelier Problem" depends on the information given in the problem and what you are trying to solve for. If you are trying to find an angle, you will likely use inverse trigonometric functions like sine inverse or cosine inverse. If you are trying to find a force, you will use regular trigonometric functions like sine or cosine.

## What are some common mistakes when solving the "Chandelier Problem"?

Some common mistakes when solving the "Chandelier Problem" include mixing up the sine and cosine functions, forgetting to use inverse trigonometric functions when solving for angles, and not carefully considering the forces acting on the chandelier. It is important to double check your calculations and diagrams to avoid these mistakes.

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