-2<\/sup>.<\/span><\/p>\nKnown :<\/u><\/span><\/p>\nSpring constant k1 <\/sub>= k2<\/sub> = k3 <\/sub>= 300 N.m-1![\"Springs](\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Springs-in-series-and-parallel-\u2013-problems-and-solutions-2.png\")
<\/sup><\/span><\/p>\nAcceleration due to gravity (g) = 10 m.s-2<\/sup><\/span><\/p>\nObject’s mass (m) = 2 kg<\/span><\/p>\nObject’s weight (w) = m g = (2)(10) = 20 Newton<\/span><\/p>\nWanted :<\/u> The change in length of the three springs (\u0394x)<\/span><\/p>\nSolution :<\/u><\/span><\/p>\nDetermine the equivalent constant :<\/span><\/p>\nSpring 1 (k1<\/sub>) and spring 2 (k2<\/sub>) are connected in parallel. The equivalent constant :<\/span><\/p>\nk12<\/sub> = k1<\/sub> + k2<\/sub> = 300 + 300 = 600 N\/m<\/span><\/p>\nSpring 3 (k3<\/sub>) and spring 12 (k12<\/sub>) are connected in series. The equivalent constant :<\/span><\/p>\n1\/k = 1\/k3<\/sub> + 1\/k12<\/sub> = 1\/300 + 1\/600 = 2\/600 + 1\/600 = 3\/600<\/span><\/p>\nk = 600\/3 = 200 N\/m<\/span><\/p>\nDetermine the change in length of the three springs :<\/span><\/p>\n\u0394x = w \/ k = 20\/200 = 2\/20 = 1\/10 = 0.1 m<\/span><\/p>\n3. Three springs are connected in series and parallel, as shown in figure below. If spring constant k = 50 Nm-1<\/sup> and a mass of 400 gram attached at one end of a spring. What is the change in length of the three springs.<\/span><\/p>\nKnown :<\/u><\/span><\/p>\nSpring constant 1 (k1<\/sub>) = k = 50 Nm-1![\"Springs](\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Springs-in-series-and-parallel-\u2013-problems-and-solutions-3.png\")
<\/sup><\/span><\/p>\nSpring constant 2 (k2<\/sub>) = k = 50 Nm-1<\/sup><\/span><\/p>\nSpring constant 3 (k3<\/sub>) = 2k = 2 (50 Nm-1<\/sup>) = 100 Nm-1<\/sup><\/span><\/p>\nObject’s mass (m) = 400 gram = 0.4 kg<\/span><\/p>\nAcceleration due to gravity (g) = 10 m\/s2<\/sup><\/span><\/p>\nObject’s weight (w) = m g = (0.4)(10) = 4 Newton<\/span><\/p>\nWanted :<\/u> The change in length (\u0394x)<\/span><\/p>\nSolution :<\/u><\/span><\/p>\nDetermine the equivalent constant :<\/span><\/p>\nSpring 1 (k1<\/sub>) and spring 2 (k2<\/sub>) are connected in parallel. The equivalent constant :<\/span><\/p>\nk12<\/sub> = k1<\/sub> + k2<\/sub> = 50 + 50 = 100 N\/m<\/span><\/p>\nSpring 3 (k3<\/sub>) and spring 12 (k12<\/sub>) are connected in series. The equivalent constant :<\/span><\/p>\n1\/k = 1\/k3<\/sub> + 1\/k12<\/sub> = 1\/100 + 1\/100 = 2\/100<\/span><\/p>\nk = 100\/2 = 50 N\/m<\/span><\/p>\nDetermine the change in length of the three springs :<\/span><\/p>\n\u0394x = w \/ k = 4 \/ 50 = = 0.08 m = 8 cm <\/span><\/p>\n\n- How does combining springs in series affect the overall spring constant?<\/strong><\/span>\n
\n- Answer:<\/strong> When springs are combined in series, the overall spring constant is reduced. The reciprocal of the equivalent spring constant is the sum of the reciprocals of the individual spring constants: 1\/k =1\/<\/span><\/span>k<\/span>1<\/span>\u200b <\/span><\/span><\/sub><\/span><\/span><\/span>\u200b<\/span><\/sub><\/span><\/span><\/span><\/span>+ 1\/<\/span><\/span>k<\/span>2<\/span><\/span><\/sub><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span><\/li>\n<\/ul>\n<\/li>\n
- How does the overall spring constant change when springs are combined in parallel?<\/strong><\/span>\n
\n- Answer:<\/strong> Combining springs in parallel results in an overall spring constant that is the sum of the individual spring constants: k \u200b<\/span><\/span><\/span><\/span><\/span>= <\/span><\/span>k<\/span>1 <\/span><\/span><\/span><\/sub>\u200b<\/span><\/span><\/span><\/span><\/span>+ <\/span><\/span>k<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/sub><\/span><\/span><\/span><\/span><\/span>.<\/span><\/li>\n<\/ul>\n<\/li>\n
- If two identical springs are arranged in series, how does the combined spring constant compare to the spring constant of an individual spring?<\/strong><\/span>\n
\n- Answer:<\/strong> The combined spring constant will be half of the spring constant of one of the individual springs.<\/span><\/li>\n<\/ul>\n<\/li>\n
- What happens to the extension or compression of springs in series when a force is applied?<\/strong><\/span>\n
\n- Answer:<\/strong> For springs in series, the same force causes each spring to extend or compress, but the total extension (or compression) is the sum of the extensions (or compressions) of the individual springs.<\/span><\/li>\n<\/ul>\n<\/li>\n
![\"Springs](\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/04\/Springs-in-series-and-parallel-\u2013-problems-and-solutions-1.png\")
<\/span><\/p>\n