Question

the height of the washington monument is measured to be 170 m on a day when the temperature is 35.0°c. assume its thermal coefficient of linear expansion is 2.5 × 10-6/°c.

Answer 1

To determine how much the height of the Washington Monument changes due to the increase in temperature, we can use the formula:

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear thermal expansion, L is the original length, and ΔT is the change in temperature.

In this case, we want to find the change in height, which is the same as the change in length along the vertical direction. Therefore, we can use the same formula to find the change in height:

Δh = αhΔT

where Δh is the change in height, α is the coefficient of linear thermal expansion, h is the original height, and ΔT is the change in temperature.

Substituting the given values, we get:

Δh = (2.5 × 10^-6/°C) × (170 m) × (35.0°C)

Δh ≈ 0.15 m

Therefore, the height of the Washington Monument increases by approximately 0.15 m when the temperature increases from 0°C to 35.0°C.