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Q.4

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A kg loudspeaker is suspended m below the ceiling by two -m-long cables that angle outward at equal angles. What is the tension in the cables?

The tension in the cable = .

See the step by step solution

Step by Step Solution

Step 1 : Tension : 

The pulling force transferred axially by a string, cable, chain, or similar item, or by each end of a rod, truss member, or similar three-dimensional object is known as tension.

Step 2 : Angle made by the cable with vertical :

Mass of a loudspeaker = kg, Distance of the loudspeaker from the ceiling = m and the length of each cable = m

The arrangement's free body diagram is seen below.

From the figure, formula to calculate the angle is,

= the cable's angle with the vertical.

= loudspeaker height from the ceiling.

= rope's length.

Substitute m for and m for to find .

Step 3 : Tension in the cable :

Mass of a loudspeaker = kg, Height of the loudspeaker from the ceiling = m and the length of each cable = m.

For the vertical equilibrium requirement, Newton's second law is used,

In the y-direction, resolving the components of forces in the ropes,

T = Tension in the cable.

= Angle made by the cable with the vertical.

= mass of the loudspeaker.

= acceleration due to gravity.

Substitute kg for , for and for to find T.

Hence, the tension in the cable = .

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