Chapter 11.2, Problem 93STP

(a)

To determine

Find the resultant spring constant.

Answer to Problem 93STP

The resultant spring constant is $4.8\text{cm}\text{/}\text{gm}$

Explanation of Solution

Given:

If one spring with constant of 12 cm per gram is attached in a series with another spring with constant of 8 cm per gram, find the resultant spring constant.

Concept Used:

The resulting spring constant k is found by the equation $\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}$

Given: $k_1=12\text{cm}\text{/}\text{gm};k_2=8\text{cm}\text{/}\text{gm}$

Calculation:

Given: $k_1=12\text{cm}\text{/}\text{gm};k_2=8\text{cm}\text{/}\text{gm}$

  $\begin{array}{l}{k}_1=12\text{cm}\text{/}\text{gm};k_2=8\text{cm}\text{/}\text{gm}\\ \frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}\\ \frac{1}{k}=\frac{1}{12}+\frac{1}{8}=\frac{2}{24}+\frac{3}{24}=\frac{5}{24}\text{cm}\text{/}\text{gm}\\ k=\frac{24}{5}\text{cm}\text{/}\text{gm}=4.8\text{cm}\text{/}\text{gm}\end{array}$

Thus, the resultant spring constant is $4.8\text{cm}\text{/}\text{gm}$

(b)

To determine

How far the object would stretch the first spring.

Answer to Problem 93STP

The object would stretch the first spring 60 cm.

Explanation of Solution

Given:

If a 5 − gram object hung from the series of springs, how far will the springs? Is this answer reasonable in this context?

Concept Used:

The answer is reasonable.

Calculation:

The answer is reasonable.

The object would stretch the first spring $5·12=60\text{cm}$ and would have to stretch the combined spring less than it would stretch either of the springs individually.

Thus, the object would stretch the first spring 60 cm.