Math / Algebra

Question3. Steel expands 11 parts in a million for each 1 degree Celsius change. Think about the 1.3 km main span of steel for the Golden Gate Bridge. If the span had no expansion joints, show that the span would be 0.21 m longer for a 15 degree Celsius increase in temperature. (Use the formula: change in $L=($ "coefficient of expansion")( initial $L$ )( change in $T$ ) ).

Studdy Solution

STEP 1

1. Steel expands 11 parts in a million per degree Celsius.
2. The initial length of the main span of the Golden Gate Bridge is 1.3 km.
3. The temperature change is 15 degrees Celsius.
4. We need to calculate the change in length of the span.

STEP 2

1. Convert units where necessary.
2. Define the variables and constants.
3. Use the formula for linear expansion.
4. Calculate the change in length.

STEP 3

Convert units where necessary.
The initial length of the span is given in kilometers. Convert this to meters for consistency in units:
$1.3 \text{ km} = 1300 \text{ m}$

STEP 4

Define the variables and constants.
- Coefficient of expansion, $\alpha = 11 \times 10^{-6}$ per degree Celsius. - Initial length, $L_0 = 1300$ m. - Change in temperature, $\Delta T = 15$ degrees Celsius.

STEP 5

Use the formula for linear expansion.
The formula for the change in length due to thermal expansion is:
$\Delta L = \alpha \cdot L_0 \cdot \Delta T$

STEP 6

Calculate the change in length.
Substitute the known values into the formula:
$\Delta L = (11 \times 10^{-6}) \cdot 1300 \cdot 15$
Calculate the product:
$\Delta L = 11 \times 10^{-6} \times 1300 \times 15$ $\Delta L = 0.2145 \text{ m}$
Round the result to two decimal places:
$\Delta L \approx 0.21 \text{ m}$
Thus, the span would be approximately $\boxed{0.21}$ meters longer for a 15 degree Celsius increase in temperature.

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Studdy Solution

STEP 1

1. Steel expands 11 parts in a million per degree Celsius.
2. The initial length of the main span of the Golden Gate Bridge is 1.3 km.
3. The temperature change is 15 degrees Celsius.
4. We need to calculate the change in length of the span.

STEP 2

1. Convert units where necessary.
2. Define the variables and constants.
3. Use the formula for linear expansion.
4. Calculate the change in length.

STEP 3

Convert units where necessary.
The initial length of the span is given in kilometers. Convert this to meters for consistency in units:
$1.3 \text{ km} = 1300 \text{ m}$

STEP 4

Define the variables and constants.
- Coefficient of expansion, $\alpha = 11 \times 10^{-6}$ per degree Celsius. - Initial length, $L_0 = 1300$ m. - Change in temperature, $\Delta T = 15$ degrees Celsius.

STEP 5

Use the formula for linear expansion.
The formula for the change in length due to thermal expansion is:
$\Delta L = \alpha \cdot L_0 \cdot \Delta T$

STEP 6

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Studdy Solution

STEP 1

1. Steel expands 11 parts in a million per degree Celsius.2. The initial length of the main span of the Golden Gate Bridge is 1.3 km.3. The temperature change is 15 degrees Celsius.4. We need to calculate the change in length of the span.

STEP 2

1. Convert units where necessary.2. Define the variables and constants.3. Use the formula for linear expansion.4. Calculate the change in length.

STEP 3

Convert units where necessary.The initial length of the span is given in kilometers. Convert this to meters for consistency in units:1.3 km=1300 m 1.3 \text{ km} = 1300 \text{ m} 1.3 km=1300 m

STEP 4

Define the variables and constants.- Coefficient of expansion, α=11×10−6 \alpha = 11 \times 10^{-6} α=11×10−6 per degree Celsius. - Initial length, L0=1300 L_0 = 1300 L0​=1300 m. - Change in temperature, ΔT=15 \Delta T = 15 ΔT=15 degrees Celsius.

STEP 5

Use the formula for linear expansion.The formula for the change in length due to thermal expansion is:ΔL=α⋅L0⋅ΔT \Delta L = \alpha \cdot L_0 \cdot \Delta T ΔL=α⋅L0​⋅ΔT

STEP 6

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Steel expands 11 parts in a million per degree Celsius.
2. The initial length of the main span of the Golden Gate Bridge is 1.3 km.
3. The temperature change is 15 degrees Celsius.
4. We need to calculate the change in length of the span.

1. Convert units where necessary.
2. Define the variables and constants.
3. Use the formula for linear expansion.
4. Calculate the change in length.

Convert units where necessary.
The initial length of the span is given in kilometers. Convert this to meters for consistency in units:
$1.3 \text{ km} = 1300 \text{ m}$

Define the variables and constants.
- Coefficient of expansion, $\alpha = 11 \times 10^{-6}$ per degree Celsius. - Initial length, $L_0 = 1300$ m. - Change in temperature, $\Delta T = 15$ degrees Celsius.

Use the formula for linear expansion.
The formula for the change in length due to thermal expansion is:
$\Delta L = \alpha \cdot L_0 \cdot \Delta T$