Consider a bimetallic strip consisting of a 0.6-mm-thick brass upper strip welded to a 0.6-mm-thick steel lower strip. When the temperature of the bimetallic strip is increased by 83 K, the unattached tip deflects by 3 mm from its original straight position, as shown in the figure. What is the length of the strip at its original position? (The linear expansion coefficients for brass and steel are 1.90 10-5 °C−1 and 1.30 10-5 °C−1, respectively.)

To solve this problem, we need to use the concept of thermal expansion and the given information about the bimetallic strip.

Step 1: Determine the change in length for each metal strip due to the increase in temperature.
The change in length for each metal strip can be calculated using the formula:

ΔL = α * L0 * ΔT

where:
- ΔL is the change in length
- α is the coefficient of linear expansion
- L0 is the original length of the strip
- ΔT is the change in temperature

For the brass strip:
ΔL_brass = α_brass * L0_brass * ΔT

For the steel strip:
ΔL_steel = α_steel * L0_steel * ΔT

Step 2: Calculate the total change in length for the bimetallic strip.
Since the upper brass strip and lower steel strip are connected, their change in length must be the same. Therefore:

ΔL_brass = ΔL_steel

α_brass * L0_brass * ΔT = α_steel * L0_steel * ΔT

Step 3: Substitute the given values into the equation and solve for the original length, L0.

α_brass * L0_brass = α_steel * L0_steel

L0_brass / L0_steel = α_steel / α_brass

L0 = (L0_brass * α_steel) / α_brass

Step 4: Substitute the values from the given information into the equation and solve for the original length, L0.

L0 = (0.6 mm * 1.30 × 10^(-5) °C^(-1)) / (1.90 × 10^(-5) °C^(-1))

L0 = 3.6 mm

Therefore, the length of the strip at its original position is 3.6 mm.

To solve this problem, we need to use the concept of linear expansion and the definition of the coefficient of linear expansion.

Linear expansion is a characteristic of most materials, where they expand or contract when their temperature changes. The coefficient of linear expansion (denoted as α) is a measure of how much a material expands or contracts per unit change in temperature.

The formula for linear expansion is:
ΔL = α * L * ΔT
where:
ΔL is the change in length of the material,
L is the original length of the material,
ΔT is the change in temperature, and
α is the coefficient of linear expansion.

In this problem, we have two different materials - brass and steel - forming a bimetallic strip. The change in length of the bimetallic strip is given as 3 mm, and the change in temperature is 83 K.

Let's assume the original length of the strip (L) is the same for both the brass and steel strips. We can set up two equations, one for brass and one for steel, and then solve for the original length (L).

For brass:
ΔL_brass = α_brass * L * ΔT

For steel:
ΔL_steel = α_steel * L * ΔT

Given that the thickness of both brass and steel strips is 0.6 mm, and the change in length of the bimetallic strip is 3 mm, we can write:
ΔL_brass = 3 mm
ΔL_steel = 3 mm

Now, let's substitute the values of the coefficients of linear expansion for brass and steel, and ΔT into the equations:

3 mm = (1.90 * 10^-5 °C^-1) * L * 83 K
3 mm = (1.30 * 10^-5 °C^-1) * L * 83 K

Now we can solve these equations to find the original length (L).

First, let's rearrange the equations to solve for L:

L = ΔL_brass / (α_brass * ΔT)
L = ΔL_steel / (α_steel * ΔT)

Now, let's substitute the given values:

L = (3 mm) / ((1.90 * 10^-5 °C^-1) * 83 K)
L = (3 mm) / ((1.30 * 10^-5 °C^-1) * 83 K)

Calculating these expressions will give us the original length (L) of the strip.