Chapter 8.5, Problem 9E

a.

To determine

To find the assembly’s force constant.

Answer to Problem 9E

The assembly’s force constant is 7238 lb/inches.

Explanation of Solution

Given information: Subway car springs takes a force of 21,714 lb to compress a coil spring assembly on a New York city Transit Authority subway car from its free height of 8 in. to its fully compressed height of 5 inches.

Calculation:

As per the given problem,

  $21714/3=7238$

Hence, the assembly’s force constant is 7238 lb/inches.

b.

To determine

To find the work done it take to compress the assembly the first half-inch.

Answer to Problem 9E

905 lb-inches work does it take to compress the assembly the first half-inch.

Explanation of Solution

Given information: Subway car springs takes a force of 21,714 lb to compress a coil spring assembly on a New York city Transit Authority subway car from its free height of 8 in. to its fully compressed height of 5 inches.

Calculation:

As per the given problem,

The amount of work it takes to compress the spring for the first half inches is,

  $\begin{array}{l}{\displaystyle {\int }_0^{0.5}7238xdx}\\ \approx 905\end{array}$

And for the second half inches,

  $\begin{array}{l}{\displaystyle {\int }_{0.5}^{1}7238xdx}\\ \approx 2714\end{array}$

Hence, 905 lb-in. work does it take to compress the assembly the first half-inch.