Answer to Question #330661 in Physics for Jane

Question

The work done on a stretching a spring it to 3.50 cm from its equilibrium length is 14.0 3. (a) How much force is required to stretch it at that

distance? (b) If a block of mass 2.75 kg moving at 4.8 m/s hits and runs into the same spring at its unstretched length, what is maximum compression of the spring?

Answer 1

Given:

$x=0.035\:\rm m$

$W=14.0\:\rm J$

(a) the required force

$$F=\frac{2W}{x}=\frac{2*14.0}{0.035}=800\:\rm N$$

(b) the stifness of a spring

$$k=\frac{F}{x}=\frac{800}{0.035}=2.29*10^4\:\rm N/m$$

hence, the maximum compression of a spring

$$x_{\max}=v\sqrt{m/k}\\ =4.8\sqrt{2.75/2.29*10^4}=0.053\:\rm m=5.3\: cm$$