A chandelier is suspended by two identical, vertical chains side by side. The chandelier's mass is m = 6.5 kg. Part (a) If the tension in one chain is represented by T, write an expression for the magnitude of the tension in terms of m and g, the gravitational acceleration on the Earth's surface. Part (b) What is the tension in one chain, T, in newtons? Part (c) If the tops of the chains are separated so that the chains are no longer vertical, does the tension increase or decrease?

a) tension on each chain T = mg/2

b) tension T = 31. 88 N

c) the tension T will increase

Explanation:

Mass of chandelier m = 6.5 Kg

acceleration due to gravity g = 9.81 m/s2

a) the total tension on the chain must be equal to the weight of the chandelier downwards.

Weight = mass x acceleration (gravity)

W = mg

Since there are two chains, this weight will be divided equally on the chains. Therefore,

Tension on each chain T = mg/2

b) tension in one chain T = mg/2

T = (6.5 x 9.81) / 2

T = 63.765/2 = 31.88 N

c) seperating the two chains will put them at an angle to the horizontal θ

The effective tension at this angle will be, T'

T' sinθ = T

i. e T' = T/sinθ

Since sinθ will be less than 90°,

T' will be greater than T

a) T = mg/2

b) T = 31. 88 N

c) Tension will increase

Explanation:

Given that m = 6.5 Kg

a)

The force due to gravity = m g

The tension in the chain = T

The total tension = 2 T

By balancing force in vertical direction

2 T = m g

T = mg/2

b)

2 T = m g

2 x T = 6.5 x 9.81

T = 31. 88 N

c)

Lets take angle made by chain is θ

So the total tension in vertical direction = 2 T cos θ

2 T cos θ = m g

T = mg / (2cos θ)

It means that tension will increase because cos θ is always less than 1.