A grandfather clock is controlled by a swinging brass pendulum that is 1.6 m long at a temperature of 28°C. (a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (Give your answer to at least four significant figures.)

1.599 m.

Explanation:

Using

α = ΔL/(LΔT) Equation 1

Where

α = Coefficient of linear expansion of brass,

ΔL = Change in length,

ΔT = Change in temperature

L = Original length.

make ΔL the subject of the equation

ΔL = α(LΔT) Equation 2

Given: L = 1.6 m, ΔT = T₂-T₁ = 0-28 = -28 ⁰C

Constant: α = 1.8×10⁻⁵/°C

Substitute into equation 2

ΔL =  (1.8×10⁻⁵)(1.6)(-28)

ΔL = -8.064×10⁻⁴ m

But,

ΔL = L₁-L

Where L = final length of the pendulum rod.

make L₁ the subject of the equation,

L₁ = ΔL+L Equation 2

L₁ = 1.6+( -8.064×10⁻⁴ )

L₁ = 1.599 m.

Explanation:

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