## Mastering Physics Solutions: Suspending a Speaker

Suspending a Speaker

Part A = 365 N

Solution Below:

A loudspeaker of mass 24.0 kg is suspended a distance of h = 1.00 below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 3.10.

Part A

What is the tension T in each of the cables?
Use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

The tension will reflect forces in both the x and y direction. The tension in the x-direction will have to cancel between the two cables, but the tension in the y direction won’t. Overall, the tension will be greater than just the force due to gravity, because it will reflect the x-contribution from each individual cable.

The force due to gravity is 9.8 * 24 = 235.2 N. This mean each cable experiences 117.6 N of vertical tension (235.2 / 2). For the x-direction, we know that the length of each cable is 3.10 m and the height is 1.0 m. This means we can solve for the angle (sin(θ) = 1.0/3.10). So θ = 18.82°. The vertical component of the tension is Ty = Tsin(θ). Since we know that Ty = 235.2 N, we can solve for T. T is just 117.6 / sin(18.82°), or 365 N.

365 N

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### 5 Responses to Mastering Physics Solutions: Suspending a Speaker

1. Shane says:

This equation is very misleading. You say Ty=Tsin(theta). Then you say solve for T. T=Ty/sin(theta) This would give you an answer of roughly 730. One needs to divide T or total answer by 2. Please clarify this in the future.

2. mario says:

i need the solution

• Mastering Physics Solutions says:

We’re confident that the posted solution is correct. If the numbers in your version of the problem are different, you could just follow our example through and you should get the correct answer. Can you be more specific?

3. Calvin says:

How can you assume Ty= 325N. what information told you that?

• Mastering Physics Solutions says:

Unfortunately that was a typo. It should have read 235 N, or 235.2 N to be precise. The answer of 365 N is correct though.