Solving Chandelier Problem: T1, Sine/Cosine Confusion

[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?

 

[danago]

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.

 

[cameuth]

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

 

[danago]

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

 

[rwisz]

[/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.