10.2. Springs http://www.ck12.org
- A spider of 0.5 g walks to the middle of her web. The web sinks by 1.0 mm due to her weight. You may
assume the mass of the web is negligible.
a. If a small burst of wind sets her in motion, with what frequency will she oscillate?
b. How many times will she go up and down in one s? In 20 s?
c. How long is each cycle?
d. Draw thexvstgraph of three cycles, assuming the spider is at its highest point in the cycle att=0 s.
Answers to Selected Problems- a. 9. 8 × 105 N/m b. 0.5 mm c. 22 Hz
- 2 × 103 N/m
- a. 110 N/m d.v(t) = ( 25 )cos(83t)
- a. 16 Hz b. 16 complete cycles but 32 times up and down, 315 complete cycles but 630 times up and down c.
0 .063 s
Investigation
- Your task: Match the period of the circular motion system with that of the spring system. You are only allowed
to change the velocity involved in the circular motion system. Consider the effective distance between the
block and the pivot to be to be fixed at 1m. The spring constant(13.5N/m) is also fixed. You should view the
charts to check whether you have succeeded. Instructions: To alter the velocity, simply click on the Select
Tool, and select the pivot. The Position tab below will allow you to numerically adjust the rotational speed
using the Motor field. To view the graphs of their respective motion in order to determine if they are in sync,
click on Chart tab below.
2.MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/4732- Now the mass on the spring has been replaced by a mass that is twice the rotating mass. Also, the distance
between the rotating mass and the pivot has been changed to 1.5 m. What velocity will keep the period the
same now?
4.MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/4733