i need help in this question
The load on each of the arrangements is L.
For each arrangement , complete the table by determining
(i) the total extension in terms of e,
(ii) the spring constant in terms of k.
Hmm......Ashish......your spring constants are ok. But am afraid the extensions are not
Anyway dude, you should know that for
spring constant,
When springs are in parallel, their net spring constants are added together. ( Same as for a capacitor and opposite to that of resistors)
When they are in series they are calculated as shown K
R = [1/k + 1/k]
-1 or 1/K
R = 1/k + 1/k
For extension,
When in series, net extension is the sum of the extension of each spring.
When in parallel, it is calculated as shown e
R = [1/e + 1/e]
-1 or 1/e
R = 1/e + 1/e
Let's back to the question now :1. Total extension will be the sum of extension by each springs when they are connected in series. Each spring extends by
eHence total extension will be
2eSpring constant will be [1/k + 1/k]
-1 =
k/22. Since the two springs are connected in parallel, total extension will be
e/2 and net spring constant will be
2ke
R = [1/e + 1/e]-1 =
e/2K
R = k + k =
2k3. Total extension :
3e/2Net spring constant :
2k/3Use the values you obtained in part(ii)
Total extension = e/2 + e = 3e/2
For the two springs in parallel, net spring constant will be 2k. Hence spring constant of the whole system will be [1/2k + 1/k]
-1 =
2k/3NOTE : k
R and e
R are the resultant spring constants and resultant extensions respectively.