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If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ?
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If two identical helical spring are connected in parallel and to these...
Deflection of a Spring System
When two identical helical springs are connected in parallel and another identical spring is connected in series, the resulting deflection of the system can be calculated using the following steps:
Step 1: Calculate the Spring Constants
The spring constant, also known as the spring rate, is a measure of the stiffness of a spring. It is defined as the force required to stretch or compress a spring by a unit distance. To calculate the spring constants of the two parallel springs and the series spring, we can use the following formula:
k = (Gd⁴)/(64nD³)
where:
- k is the spring constant
- G is the modulus of rigidity of the material (in N/m²)
- d is the wire diameter of the spring (in m)
- n is the number of coils in the spring
- D is the mean diameter of the spring (in m)
Step 2: Calculate the Equivalent Spring Constant of the Parallel Springs
When two identical springs are connected in parallel, the equivalent spring constant is given by:
k_parallel = k₁ + k₂
where k₁ and k₂ are the spring constants of the individual springs.
Step 3: Calculate the Equivalent Spring Constant of the Series Spring
When two identical springs are connected in series, the equivalent spring constant is given by:
k_series = (k₁k₂)/(k₁ + k₂)
Step 4: Calculate the Deflection of the System
The deflection of the system can be calculated using the following formula:
x = W/(k_parallel + k_series)
where:
- x is the deflection of the system (in m)
- W is the weight applied to the system (in N)
- k_parallel is the equivalent spring constant of the parallel springs (in N/m)
- k_series is the equivalent spring constant of the series spring (in N/m)
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If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ?
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If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ?.
If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two identical helical spring are connected in parallel and to these two, another identical spring is connected in series and the system is loaded by a weight W, as shown in the figure, then the resulting deflection will be given by ?.
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