Chapter 3.5, Problem 38AYU

To determine

Least compression required of the spring.

Answer to Problem 38AYU

Least compression required of the spring is $x=3.94ft$ .

Explanation of Solution

Given information:

  $W=\frac{1}{2}k{x}^2$

Work done by body motion is given as, $\tilde{W}=\frac{w}{2g}{\nu }^2$

Calculation:

First there is need to convert $25mph$ to $ft/\sec$

  $25\min /hr\times \left(5280ft/1ml\right)\times \left(\frac{1hr}{3600\sec }\right)=36.67ft/\sec$

One want all the energy from the moving car to be stored in the spring:

  $\left(\frac{1}{2}\right)w{v}^2=$ Kinetic enrgy of the car.

  $\left(\frac{1}{2}\right)k{x}^2=$ Potential energy of the spring.

  $\begin{array}{l}\left(\frac{1}{2}\right)w{v}^2=\left(\frac{1}{2}\right)k{x}^2\\ w{v}^2=k{x}^2\\ \left(4000lb\right){\left(36.67ft/\sec \right)}^2=\left(9450lb/ft\right){\left(x\right)}^2\\ x=3.94ft\end{array}$