Final answer:
Calculating the change in height of the Washington Monument due to thermal expansion using the coefficient for marble, the estimated new height on a cooler day is approximately 165.7925 meters. The closest option to this value without exceeding it is option (c) 160.8 meters.
Step-by-step explanation:
The student's question pertains to the physical concept of thermal expansion, which refers to the change in size of an object due to temperature variations. Specifically, we are considering the change in height of the Washington Monument, made of limestone, but for the calculation, we will use the coefficient of thermal expansion α typical for marble. The formula to calculate the change in height (ΔL) is:
ΔL = α × L0 × ΔT
Where:
α = Coefficient of thermal expansion for marbleL0 = Original height of the object ΔT = Change in temperature
The coefficients of thermal expansion for common materials are widely available and the one for marble can be found in scientific reference materials. For marble, α is typically around 5.5×10-6 /°C. Now to calculate the change in height due to the temperature change from 35.0°C to -10.0°C, which is a 45.0°C decrease:
ΔL = (5.5×10-6 /°C) × (170 m) × (-45.0°C)
ΔL = -4.2075 m
This result tells us that the Washington Monument would contract by approximately 4.2075 meters due to the decrease in temperature. To find the new height, we subtract this from the original height:
New height = L0 - ΔL = 170 m - 4.2075 m = 165.7925 m
Since none of the provided options exactly match our calculated height, we need to choose only one option that is closest without going over the calculated height. Therefore, the best fitting option from the choices provided would be:
(c) 160.8 m
Option (c) is not the calculated height, but it is the closest option that does not exceed the calculated value.