11) A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0° C. The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are 2.0 x10-5 K-1 (brass) and 2.4 x 10-5 K-1 (aluminum). -120.0 cm aluminum B) 420°C C) 510°C D) 470°C E) 440°C brass A) 490°C
Theory and Design for Mechanical Measurements
Measurement is a term that refers to analyzing a manufactured component regarding the degree of accuracy for dimensions, tolerances, geometric profile, roundness, flatness, smoothness, etc. Measurement always involves comparing the manufactured component or the prototype with a standard specimen whose dimensions and other parameters are assumed to be perfect and do not undergo changes with respect to time.Precisely in mechanical engineering the branch that deals with the application of scientific principles for measurements is known as metrology. The domain of metrology in general deals with various measurements like mechanical, chemical, thermodynamic, physical, and biological measurements. In mechanical engineering, the measurements are limited to mechanical specific such as length, mass, surface profile, flatness, roundness, viscosity, heat transfer, etc.
Basic principles of engineering metrology
Metrology is described as the science of measurement, precision, and accuracy. In other words, it is a method of measurement based on units and predefined standards.
Please show all calculations and type them out So that I will be able to read them and understand what you're saying I have bad eyesight and it is very difficult for me to read handwriting
![**Expansion of Brass and Aluminum Rods with Temperature Increase**
**Problem Statement:**
11) A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0° C. The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are 2.0 × 10⁻⁵ K⁻¹ (brass) and 2.4 × 10⁻⁵ K⁻¹ (aluminum).
The schematic diagram represents two rod segments (one of brass and one of aluminum) separated by a gap of 1.2 cm. The entire setup maintains a total length of 120.0 cm.
**Options:**
A) 490°C
B) 420°C
C) 510°C
D) 470°C
E) 440°C
**Explanation of Diagram:**
- **Brass rod**
- Initial Length: 69.5 cm
- **Aluminum rod**
- Initial Length: 49.3 cm
- **Total Distance Maintained:** 120.0 cm
- **Initial Gap Between Rods:** 1.2 cm
The purpose is to calculate the temperature at which the two rods, upon expanding due to the rise in temperature, will barely touch each other.
**Key Concepts:**
- **Linear Expansion Formula:**
\[
\Delta L = L_0 \alpha \Delta T
\]
where \( L_0 \) is the initial length, \( \alpha \) is the coefficient of linear expansion, and \( \Delta T \) is the change in temperature.
Given Data:
- \( \alpha_{brass} = 2.0 \times 10^{-5} \, \text{K}^{-1} \)
- \( \alpha_{aluminum} = 2.4 \times 10^{-5} \, \text{K}^{-1} \)
**Solution Approach:**
1. Calculate the individual expansions of brass and aluminum rods as they are heated.
2. Sum these](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f72c006-9b48-426b-aa7e-60007b6c336c%2Fbd162e85-f340-498c-9086-a779f5a695fa%2Fm6ocjm_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
