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Chapter 6: Problem 51

A certain amount of work is required to stretch spring A a certain distance. Twice as much work is required to stretch spring B half that distance. Compare the spring constants of the two.

Short Answer

Expert verified
The spring constant of spring B is 8 times that of spring A.

Step by step solution

01

Define the equation for spring A

First, we need to define the work equation for spring A. It is given by W_A = (1/2)k_Ax^2, where W_A is the work done on spring A, k_A is the spring constant of A, and x is the distance the spring is stretched.
02

Define the equation for spring B

Similarly, the work equation for spring B is given by W_B = (1/2)k_B(x/2)^2, where W_B is the work done on spring B, k_B is the spring constant of B, and x/2 is the distance (half the distance of spring A) the spring is stretched.
03

Relate the equations

Since it is stated that twice as much work is required to stretch spring B half the distance, we can say that W_B = 2W_A. Substituting the expressions for W_A and W_B obtained from steps 1 and 2 into this equation, we get: (1/2)k_B(x/2)^2 = 2(1/2)k_Ax^2
04

Simplify for comparison

Solving this equation, we get, k_B = 8k_A.

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Most popular questions from this chapter

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