{"id":1167,"date":"2022-03-24T11:30:39","date_gmt":"2022-03-24T11:30:39","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=1167"},"modified":"2022-03-24T05:41:21","modified_gmt":"2022-03-24T05:41:21","slug":"work-done-by-variable-force","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/work-done-by-variable-force\/","title":{"rendered":"\u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4\u0995\u09be\u099c (Work Done by A Variable Force)"},"content":{"rendered":"

\u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4\u0995\u09be\u099c (Work Done by A Variable Force)<\/b><\/h2>\n

\u09ac\u09b2 \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf, \u09a4\u09be\u0987 \u098f\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09ae\u09be\u09a8 \u09ac\u09b0\u09be\u09ac\u09b0, \u09a6\u09bf\u0995 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09be \u0989\u09ad\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u0987 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u0995\u09c7\u09ac\u09b2 \u09ae\u09be\u09a8\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09ac\u0964<\/span><\/p>\n

\"variable-force\"<\/p>\n

\u00a0<\/span>\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u09ac\u09b2 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b6\u09c0\u09b2\u0964 \u09af\u09c7 \u09a6\u09bf\u0995\u09c7 \u09ac\u09b2 \u0995\u09cd\u09b0\u09bf\u09df\u09be \u0995\u09b0\u09c7 \u09b8\u09c7\u0987 \u09a6\u09bf\u0995\u0995\u09c7 \u0986\u09b2\u09cb\u099a\u09a8\u09be\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09b0\u09be <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7 \u09b0\u09c2\u09aa\u09c7 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09bf\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u098f\u0987 \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09df <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2<\/span>\u0964 <\/span>\u098f \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 x_{i}<\/span><\/span> \u09a5\u09c7\u0995\u09c7 \u09b6\u09c7\u09b7 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 x_{f}<\/span><\/span>\u00a0-\u098f \u09af\u09be\u0993\u09df\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09ac\u09cb\u0964 \u098f \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09b0\u09be \u09ae\u09cb\u099f \u09b8\u09b0\u09a3<\/a>\u0995\u09c7 <\/span>x<\/span> \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u09c7\u09b0 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 <\/span>N<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09b8\u09ae\u09be\u09a8 \u0985\u0982\u09b6\u09c7 \u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09bf (\u099a\u09bf\u09a4\u09cd\u09b0)\u0964\u00a0 <\/span><\/p>\n

\u098f \u0985\u0982\u09b6\u0997\u09c1\u09b2\u09cb\u09b0 \u09aa\u09cd\u09b0\u09a5\u09ae\u099f\u09bf \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u0995, \u09af\u09c7\u0996\u09be\u09a8\u09c7 x_{i}<\/span> <\/span>\u09a5\u09c7\u0995\u09c7 x_{i}+\\Delta x<\/span> <\/span>\u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7 \\Delta x<\/span><\/span>\u0964 <\/span>\u098f \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3\u0995\u09be\u09b2\u09c7 \u09ac\u09b2 <\/span>F(x)<\/span><\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09b2\u09c7\u0993, \u09b8\u09b0\u09a3 \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u0996\u09c1\u09ac\u0987 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0, \u09a4\u09be\u0987 \u0986\u09ae\u09b0\u09be \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8\u09c7\u09b0 \u098f\u0987 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09a8\u0997\u09a3\u09cd\u09af \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09c7 \u09ac\u09b2\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf \u098f \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3 \u0995\u09be\u09b2\u09c7 \u09ac\u09b2 F(x)<\/span><\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, F(x)<\/span><\/span> \u098f\u09b0 \u098f \u09a7\u09cd\u09b0\u09c1\u09ac \u09ae\u09be\u09a8 F_{1}<\/span><\/span>\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098f \u0985\u0982\u09b6\u09c7 \u098f \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09be\u099c \\Delta W_{1}<\/span><\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09aa\u09cd\u09b0\u09be\u09df,<\/span><\/p>\n\\Delta W_{1}=F_{1} \\Delta x <\/span>\n

\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0985\u0982\u09b6\u09c7 x_{i}+\\Delta x<\/span><\/span>\u09a5\u09c7\u0995\u09c7 x_{i}+2 \\Delta x<\/span><\/span> \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3\\Delta x<\/span><\/span>\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, \u00a0F(x)<\/span><\/span> \u098f\u09b0 \u098f\u0987 \u0985\u0982\u09b6\u09c7 \u09aa\u09cd\u09b0\u09be\u09df \u09a7\u09cd\u09b0\u09c1\u09ac \u09ae\u09be\u09a8 F_{2}<\/span><\/span>\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0985\u0982\u09b6\u09c7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09b9\u09ac\u09c7 \u09aa\u09cd\u09b0\u09be\u09df \\Delta W_{2}=F_{2} \\Delta x<\/span><\/span>\u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 x_{i}<\/span> <\/span>\u09a5\u09c7\u0995\u09c7 x_{f}<\/span><\/span> \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09b8\u09b0\u09be\u09a4\u09c7 F(x)<\/span> <\/span>\u00a0\u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u09ae\u09cb\u099f \u0995\u09be\u099c \u09b9\u09ac\u09c7<\/span>\u00a0<\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u0985\u09a8\u09c1\u09b0\u09c2\u09aa <\/span>N<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09aa\u09a6\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u09b0 \u09aa\u09cd\u09b0\u09be\u09df \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982<\/span><\/p>\n\\begin{aligned}\n\nW &=\\Delta W_{1}+\\Delta W_{2}+\\Delta W_{3}+\\cdots+\\Delta W_{N} \\\\\n\n&=F_{1} \\Delta x+F_{2} \\Delta x+F_{3} \\Delta x+\\cdots+F_{N} \\Delta x\n\n\\end{aligned}<\/span>\n

\u09ac\u09be, W=\\sum_{k=1}^{N} F_{k} \\Delta x <\/span><\/span><\/p>\n

\\Delta x<\/span><\/span> \u0995\u09c7 \u09af\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0\u09a4\u09b0 \u09a4\u09a5\u09be \u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0985\u0982\u09b6\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09af\u09a4 \u09ac\u09c3\u09b9\u09ce \u09a5\u09c7\u0995\u09c7 \u09ac\u09c3\u09b9\u09a4\u09cd\u09a4\u09b0 \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7 \u09b9\u09bf\u09b8\u09be\u09ac\u0995\u09c3\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a4\u09a4\u09cb \u09b8\u09a0\u09bf\u0995 \u0995\u09be\u099c\u09c7\u09b0 \u09ae\u09be\u09a8\u09c7\u09b0 \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u09aa\u09cc\u0981\u099b\u09be\u09ac\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u09ac\u09b2 F(x)<\/span><\/span>\u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09b8\u09a0\u09bf\u0995 \u09ae\u09be\u09a8 \u09aa\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf \u09af\u09a6\u09bf \u0986\u09ae\u09b0\u09be \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7\u09b0 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 <\/span>x<\/span> \u0995\u09c7 \u09b6\u09c2\u09a8\u09cd\u09af \u098f\u09ac\u0982 \u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0985\u0982\u09b6\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>N<\/span> \u0995\u09c7 \u0985\u09b8\u09c0\u09ae \u0995\u09b0\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u09b8\u09a0\u09bf\u0995 \u09ab\u09b2 \u09b9\u09ac\u09c7,<\/span><\/p>\nW=\\lim _{\\Delta x \\rightarrow 0} \\sum_{k=1}^{N} F_{k} \\Delta x<\/span>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \\lim _{\\Delta x \\rightarrow 0} \\sum_{k=1}^{N} F_{k} \\Delta x<\/span><\/span>\u00a0\u09b0\u09be\u09b6\u09bf\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8\u09c7\u09b0 \u09ad\u09be\u09b7\u09be\u09df<\/span><\/p>\n

\\int_{x_{i}}^{x_{f}} F(x) d x<\/span> \u09af\u09be x_{i}<\/span><\/span> \u09a5\u09c7\u0995\u09c7 x_{f}<\/span><\/span>\u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 <\/span>x<\/span> \u098f\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 <\/span>F(x)<\/span> \u098f\u09b0 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3 \u09ac\u09be \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a6\u09be\u0981\u09dc\u09be\u09df,<\/span><\/p>\nW=\\int_{x_{i}}^{x_{f}} F(x) d x<\/span>\n

\u09b8\u0982\u0996\u09cd\u09af\u09be\u0997\u09a4\u09ad\u09be\u09ac\u09c7 \u098f\u0987 \u09b0\u09be\u09b6\u09bf\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7 \u09ac\u09b2 \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be (force curve) \u098f\u09ac\u0982x_{i}<\/span> <\/span>\u00a0\u0993x_{f}<\/span> <\/span>\u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 X-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 (\u099a\u09bf\u09a4\u09cd\u09b0)\u0964<\/span><\/p>\n

\u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c : \u09a6\u09cd\u09ac\u09bf\u09ae\u09be\u09a4\u09cd\u09b0\u09bf\u0995 \u0998\u099f\u09a8\u09be \u09ac\u09be \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09c2\u09aa(Work Done by a Variable Force: Two Dimensional Case or Vector Form)<\/b><\/h2>\n

\u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be\u09b0 \u0989\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b6\u09c0\u09b2 \u09ac\u09b2 <\/span>F<\/span> \u09a6\u09bf\u0995\u09c7 \u098f\u09ac\u0982 \u09ae\u09be\u09a8\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u098f\u09ac\u0982 \u0995\u09a3\u09be\u099f\u09bf \u098f\u0995\u099f\u09bf \u09ac\u0995\u09cd\u09b0\u09aa\u09a5\u09c7 (curved path) \u099a\u09b2\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u098f\u0987 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09be\u099c \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09b0\u09be \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5\u0995\u09c7 \u09ac\u09bf\u09aa\u09c1\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3 <\/span>\u2206S<\/span><\/em>-\u098f \u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09bf\u0964 \u098f\u09b0\u09c2\u09aa \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u09b8\u09b0\u09a3\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u09b9\u099a\u09cd\u099b\u09c7 \u0997\u09a4\u09bf\u09aa\u09a5\u09c7\u09b0 \u09b8\u0982\u09b6\u09cd\u09b2\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09aa\u09a5\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u0997\u09a4\u09bf\u09b0 \u09a6\u09bf\u0995\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u09ac\u09b0\u09be\u09ac\u09b0\u0964 \u09a8\u09bf\u099a\u09c7\u09b0 \u099a\u09bf\u09a4\u09cd\u09b0\u09c7 \u098f\u09b0\u09c2\u09aa \u09a6\u09c1\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09ac\u09be\u099a\u09bf\u09a4 \u09b8\u09b0\u09a3 \u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7\u0964 \u098f\u0987 \u099a\u09bf\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09ac\u09b2 <\/span>F<\/span> \u098f\u09ac\u0982 <\/span>F<\/span> \u0993 <\/span>\u2206S<\/span><\/em> \u098f\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ad\u09c1\u0995\u09cd\u09a4 \u0995\u09cb\u09a3 <\/span><\/p>\n

\"variable-force-two-dimentional\"<\/p>\n

\u09a6\u09c7\u0996\u09be \u09af\u09be\u099a\u09cd\u099b\u09c7, <\/span>\u2206S<\/span><\/em> \u09b8\u09b0\u09a3 \u0995\u09be\u09b2\u09c7 \u0995\u09a3\u09be\u09b0 \u0989\u09aa\u09b0 <\/span>F<\/span> \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09be\u099c <\/span>W<\/span> \u0986\u09ae\u09b0\u09be \u09a8\u09bf\u09ae\u09cd\u09a8\u09cb\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf,<\/span><\/p>\n

W=FS<\/em><\/strong><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>F<\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u0986\u09ae\u09b0\u09be \u09af\u09c7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09b8\u09b0\u09a3 <\/span>\u2206S<\/span><\/em> \u09a6\u09bf\u09df\u09c7\u099b\u09bf \u09b8\u09c7\u0987 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b6\u09c0\u09b2 \u09ac\u09b2\u0964 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>i<\/span> \u09a5\u09c7\u0995\u09c7 \u09b6\u09c7\u09b7 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>f<\/span>-\u098f \u09af\u09be\u0993\u09df\u09be \u0995\u09be\u09b2\u09c7 (\u099a\u09bf\u09a4\u09cd\u09b0) \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 <\/span>F<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0989\u09aa\u09b0 \u0995\u09c3\u09a4 \u0995\u09be\u099c <\/span>W<\/span> \u09b9\u09ac\u09c7 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u09b0\u09c7\u0996\u09be\u0982\u09b6\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09c3\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09be\u099c\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf,<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce, W=\\sum \\Delta W=\\sum \\overrightarrow{\\mathrm{F}} \\cdot \\Delta \\overrightarrow{\\mathrm{S}}==F \\Delta S \\cos \\sum \\theta<\/span><\/span><\/p>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u09b0\u09c7\u0996\u09be\u0982\u09b6 <\/span>\u2206S-<\/span>\u0997\u09c1\u09b2\u09cb \u09af\u09a6\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0\u09be\u09a4\u09bf\u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b9\u09df, \u09a4\u09be\u09b9\u09b2\u09c7 \u098f\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u0995 (differential) <\/span>dS<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u098f\u09ac\u0982 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u0995\u09c7 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09df\u0964 \u09ab\u09b2\u09c7<\/span>\u00a0<\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a6\u09be\u0981\u09dc\u09be\u09df,<\/span><\/p>\nW=\\int d W=\\int_{i}^{f} \\overrightarrow{\\mathrm{F}} \\cdot d \\overrightarrow{\\mathrm{S}}<\/span>\n

\u098f\u0987 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09a4\u09c7 \u09b9\u09b2\u09c7 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09b2 <\/span>F<\/span> \u098f\u09ac\u0982 <\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09c0\u09ad\u09be\u09ac\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u099a\u09cd\u099b\u09c7 \u09a4\u09be \u099c\u09be\u09a8\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 <\/span>F<\/span> \u098f\u09ac\u0982 <\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a3\u09be\u099f\u09bf\u09b0 <\/span>x<\/span> \u098f\u09ac\u0982 <\/span>y<\/span> \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0982\u0995\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4\u0995\u09be\u099c (Work Done by A Variable Force) \u09ac\u09b2 \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf, \u09a4\u09be\u0987 \u098f\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09ae\u09be\u09a8 \u09ac\u09b0\u09be\u09ac\u09b0, \u09a6\u09bf\u0995 \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09be \u0989\u09ad\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u0987 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u0995\u09c7\u09ac\u09b2 \u09ae\u09be\u09a8\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09ac\u0964 \u00a0\u09a7\u09b0\u09be \u09af\u09be\u0995,<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4239,3028,50,51],"tags":[],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1167"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=1167"}],"version-history":[{"count":9,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1167\/revisions"}],"predecessor-version":[{"id":12404,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1167\/revisions\/12404"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=1167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=1167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=1167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}