# Solving Problems with Newton's Laws - Hanging Chandelier

• tiggrulz13
In summary: T1but T1 is still in the answerIn summary, to find the tension in cable 1, T1, that does not depend on T2, we can use the two equations ΣFx = 0 and ΣFy = 0 to eliminate T2. After solving for T1, the final expression is mg/sin(θ1) + tan(θ2)cos(θ1).
tiggrulz13

## Homework Statement

A chandelier with mass m 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 T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling.
Find an expression for T1, the tension in cable 1, that does not depend on T2.
Express your answer in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g.

## The Attempt at a Solution

So far I have found the x and y components:

ΣFx = 0 = -T1cosθ1 + T2cosθ2
ΣFy = 0 = T1sinθ1 + T2sinθ2 - mg

Now I need to eliminate T2 from this pair of equations and solve for T1, but I can't figure out how to do this.

tiggrulz13 said:

## Homework Statement

A chandelier with mass m 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 T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling.
Find an expression for T1, the tension in cable 1, that does not depend on T2.
Express your answer in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g.

## The Attempt at a Solution

So far I have found the x and y components:

ΣFx = 0 = -T1cosθ1 + T2cosθ2
ΣFy = 0 = T1sinθ1 + T2sinθ2 - mg

Now I need to eliminate T2 from this pair of equations and solve for T1, but I can't figure out how to do this.

2 equations - 4 unknowns T1 and T2, θ1, θ2?

You can't get rid of T2?

Try harder. You know directly that T2 = T1*(Cosθ1/Cosθ2)

Surely something will occur to you.

I tried that, but I kept getting an answer where T1 was equal to something that had T1 in it. Such as:

T1 = (mg - T1cosθ1tanθ2) / sinθ1

I got that when I plugged T2 = T1 (cosθ1)/(cosθ2) into the y component.

tiggrulz13 said:
I tried that, but I kept getting an answer where T1 was equal to something that had T1 in it. Such as:

T1 = (mg - T1cosθ1tanθ2) / sinθ1

I got that when I plugged T2 = T1 (cosθ1)/(cosθ2) into the y component.

And this is a problem because ...?

Is it allowed to have T1 in the answer? I didn't think it was because it said in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g. It never mentions T1.

T1 is not suppose t be in the answer. i have the same question for my assignment. the answer ends up being :
mg/sin(theta1)+tan(theta2)*cos(theta1)

i too substituted T2 = T1 (cosθ1)/(cosθ2) for T2 in the second equation and got

0=T1sin(theta1)+T1(cos(theta1)*sin(theta2)/cos(theta2))-mg

after moving the mg to the other side i made the sin(theta2)/cos(theta2)= tan(theta2), and then factored out the two.

mg=T1(sin(theta1)+tan(theta2)cos(theta1)

devided both sides by sin(theta1)+tan(theta2)cos(theta1)
and got
mg/sin(theta1)+tan(theta2)*cos(theta1)

## What are Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental physical laws that describe the behavior of objects in motion. The first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. The second law explains how the velocity of an object changes when a force is applied to it. The third law states that for every action, there is an equal and opposite reaction.

## How can Newton's Laws be applied to solve problems?

Newton's Laws can be applied to solve problems by breaking down the problem into smaller components and using the laws to analyze the forces acting on each component. By understanding how forces interact and affect motion, we can determine the net force on an object and predict its motion.

## How can Newton's Laws be used to solve a problem involving a hanging chandelier?

To solve a problem involving a hanging chandelier, we can use Newton's Laws to analyze the forces acting on the chandelier. The weight of the chandelier and the tension in the chain holding it up are two forces that are important to consider. By using the second law, we can determine the net force on the chandelier and predict its motion.

## What are some common challenges when solving problems with Newton's Laws?

Some common challenges when solving problems with Newton's Laws include accurately identifying all the forces acting on an object, accounting for the direction and magnitude of the forces, and understanding how forces can change as an object moves. It is also important to use proper units and apply the laws correctly to get accurate results.

## How can understanding Newton's Laws be useful in everyday life?

Understanding Newton's Laws can be useful in everyday life by helping us to understand how objects move and interact with each other. This knowledge can be applied to various situations, such as driving a car, playing sports, or even just walking. It also allows us to predict and explain the motion of objects, which is essential in many engineering and design fields.

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