{"id":28596,"date":"2024-09-16T13:00:52","date_gmt":"2024-09-16T13:00:52","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28596"},"modified":"2025-09-18T00:42:30","modified_gmt":"2025-09-18T00:42:30","slug":"%e0%a4%95%e0%a4%be%e0%a4%b0%e0%a5%8d%e0%a4%af-%e0%a4%94%e0%a4%b0-%e0%a4%af%e0%a4%be%e0%a4%82%e0%a4%a4%e0%a5%8d%e0%a4%b0%e0%a4%bf%e0%a4%95-%e0%a4%8a%e0%a4%b0%e0%a5%8d%e0%a4%9c%e0%a4%be","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%95%e0%a4%be%e0%a4%b0%e0%a5%8d%e0%a4%af-%e0%a4%94%e0%a4%b0-%e0%a4%af%e0%a4%be%e0%a4%82%e0%a4%a4%e0%a5%8d%e0%a4%b0%e0%a4%bf%e0%a4%95-%e0%a4%8a%e0%a4%b0%e0%a5%8d%e0%a4%9c%e0%a4%be\/","title":{"rendered":"\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0939\u092e \u0907\u0938 \u0915\u0915\u094d\u0937\u093e\u0913\u0902 \u0915\u0940 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0915\u094b \u0915\u093e\u0930\u094d\u092f, \u090a\u0930\u094d\u091c\u093e, \u0914\u0930 \u0909\u0928\u0915\u0940 \u0915\u0941\u091b \u0930\u0942\u092a\u094b\u0902: \u0917\u0924\u093f\u091c \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u0930\u094d\u092a\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0907\u0928 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u094b\u0902 \u0938\u0947 \u0939\u092e \u090f\u0915 \u091a\u0932 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 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style=\"text-align:left;\">\n<li><strong>\u0938\u092e\u091d\u0928\u093e<\/strong> \u0915\u093f \u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0915\u094d\u092f\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u091c\u0940\u0935\u093f\u0924 \u092c\u0932 \u092a\u094d\u0930\u092e\u0947\u092f<\/strong> \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e \u0924\u093e\u0915\u093f \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u092e\u0947\u0902 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u094b \u0938\u092e\u091d\u093e \u091c\u093e \u0938\u0915\u0947\u0964<\/li>\n<li><strong>\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/strong> \u0915\u0930\u0928\u093e \u0915\u093f \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u0938\u093e\u0925 \u0915\u0948\u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/li>\n<\/ol>\n<p><strong>\u0938\u0942\u091a\u0940<\/strong><br \/>\n<a href=\"#1\">\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/a><br \/>\n<a href=\"#11\">\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927<\/a><br \/>\n<a href=\"#12\">\u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0914\u0930 \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940<\/a><br \/>\n<a href=\"#2\">\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/a><br \/>\n<a href=\"#21\">\u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0914\u0930 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0917\u093f\u0930\u093e\u0935\u091f<\/a><\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/_q-5C4FQOaU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/h2>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_q-5C4FQOaU&amp;t=130s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u092c 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\u0932\u093f\u090f, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092e\u0947\u0902 \u00ab\u0915\u0941\u091b \u0928\u092f\u093e\u00bb \u091c\u094b\u0921\u093c\u0928\u093e \u092a\u0921\u093c\u0924\u093e \u0939\u0948: \u0935\u0939 \u00ab\u0915\u0941\u091b\u00bb \u091c\u093f\u0938\u0947 \u0939\u092e \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align:justify;\">\u0905\u092c \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0926\u094b \u092d\u094c\u0924\u093f\u0915 \u092e\u093e\u0924\u094d\u0930\u093e\u090f\u0902 \u0939\u0948\u0902 \u091c\u094b \u0915\u093f\u0938\u0940 \u092d\u094c\u0924\u093f\u0915 \u0935\u0938\u094d\u0924\u0941 \u092f\u093e \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902: \u0935\u0939 \u0939\u0948 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u0935\u0947\u0917, \u091c\u093f\u0938\u0947 \u0939\u092e \u0905\u091a\u094d\u091b\u0940 \u0924\u0930\u0939 \u091c\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u091c\u094b \u0917\u0924\u093f \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948, \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u091c\u093f\u0938\u0947 \u0939\u092e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u093e \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u091c\u094b \u092b\u093f\u0932\u0939\u093e\u0932 <em>\u0935\u0939 \u0926\u0930\u094d\u0936\u093e\u090f\u0917\u0940 \u091c\u094b \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0906\u0930\u093e\u092e \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 \u0907\u0938 \u0917\u0924\u093f \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u0932\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u091c\u094b\u0921\u093c\u0928\u093e \u092a\u0921\u093c\u093e \u0939\u0948\u0964<\/em><\/p>\n<p><a name=\"11\"><\/a><\/p>\n<h3>\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927<\/h3>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_q-5C4FQOaU&amp;t=865s\" target=\"_blank\" rel=\"noopener\"><strong>\u0906\u0907\u090f \u092c\u094d\u0932\u0949\u0915 \u0914\u0930 \u092c\u0932 \u092a\u0930 \u0935\u093e\u092a\u0938 \u091c\u093e\u090f\u0902<\/strong><\/a> \u091c\u094b \u0907\u0938\u0947 \u0917\u0924\u093f \u092e\u0947\u0902 \u0932\u093e\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u092c\u0932 \u0917\u0924\u093f \u0928\u0939\u0940\u0902 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0909\u0938\u0928\u0947 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u092e\u0947\u0902 \u0915\u0941\u091b \u092d\u0940 \u0928\u0939\u0940\u0902 \u091c\u094b\u0921\u093c\u093e \u0939\u0948, \u091c\u092c\u0915\u093f \u092f\u0926\u093f \u0910\u0938\u093e \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0909\u0938\u0928\u0947 <strong>\u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/strong> \u091c\u094b\u0921\u093c\u0940 \u0939\u0948\u0964 \u091c\u092c \u0917\u0924\u093f \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b \u0936\u0930\u0940\u0930 \u0915\u094b \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092e\u093e\u0930\u094d\u0917 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930\u0928\u093e \u092a\u0921\u093c\u0924\u093e \u0939\u0948 \u0914\u0930 \u091c\u092c \u0924\u0915 \u092f\u0939 \u0915\u0930\u0924\u093e \u0939\u0948, \u092c\u0932 \u090a\u0930\u094d\u091c\u093e \u091c\u094b\u0921\u093c\u0947\u0917\u093e\u0964 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u091c\u094b\u0921\u093c\u0928\u0947 \u092f\u093e \u0918\u091f\u093e\u0928\u0947 \u0915\u0940 \u0907\u0938 \u0915\u094d\u0930\u093f\u092f\u093e \u0915\u094b \u0939\u092e \u00ab\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0928\u093e\u00bb \u0915\u0939\u0947\u0902\u0917\u0947, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 <strong>\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0915\u093e\u0930\u094d\u092f \u0915\u0947 \u0924\u0924\u094d\u0935 <span class=\"katex-eq\" data-katex-display=\"false\">dW<\/span> \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/strong><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{lr}\n\n    dW =\\vec{F} \\cdot d\\vec{r} &amp; (1)\n\n    \\end{array}<\/span>\n<\/p>\n<p style=\"text-align:justify;\">\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}<\/span> \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u092c\u0932 \u0939\u0948 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d\\vec{r}<\/span> \u0935\u0939 \u0935\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0924\u0924\u094d\u0935 \u0939\u0948 \u091c\u093f\u0938 \u092a\u0930 \u092c\u0932 \u0928\u0947 \u0915\u093e\u0930\u094d\u092f \u0915\u093f\u092f\u093e \u0939\u0948\u0964 \u091a\u0942\u0902\u0915\u093f \u092f\u0939 \u092c\u0932 \u090f\u0915 \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">m,<\/span> \u0915\u0947 \u0936\u0930\u0940\u0930 \u092a\u0930 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u0947 <a href=\"https:\/\/toposuranos.com\/las-leyes-de-newton\/\" target=\"_blank\" rel=\"noopener\">\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0928\u093f\u092f\u092e<\/a> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0939\u092e \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{lr}\n\n    \\displaystyle\\vec{F} =\\frac{d\\vec{p}}{dt} = m\\frac{d\\vec{v}}{dt} &amp; (2)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0914\u0930 (2) \u0938\u0947 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    dW &amp; \\displaystyle =m\\frac{d\\vec{v}}{dt} \\cdot d\\vec{r} = m\\frac{d\\vec{r}}{dt} \\cdot d\\vec{v} = m\\vec{v} \\cdot d\\vec{v} &amp; (3)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u0907\u0938 \u0905\u0902\u0924\u093f\u092e \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u094b \u090f\u0915\u0940\u0915\u0943\u0924 \u0915\u0930\u0915\u0947 \u0915\u0941\u0932 \u0915\u093e\u0930\u094d\u092f \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0902\u0917\u0947:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    W &amp; = \\displaystyle {\\int_{i}^{f}} m\\vec{v} \\cdot d\\vec{v} = \\left.\\frac{1}{2}m \\|\\vec{v}\\|^2 \\right|_i^f &amp; \\\\ \\\\\n\n    &amp; \\displaystyle = \\frac{1}{2}m \\|\\vec{v}_f\\|^2 - \\frac{1}{2}m\\|\\vec{v}_i\\|^2 &amp; (4)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u0907\u0938 \u0924\u0930\u094d\u0915 \u0938\u0947, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0915\u093e\u0930\u094d\u092f \u0926\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0905\u0935\u0938\u094d\u0925\u093e\u0913\u0902 \u092e\u0947\u0902 \u090f\u0915 \u0939\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948, \u090f\u0915 \u0905\u0902\u0924\u093f\u092e \u0905\u0935\u0938\u094d\u0925\u093e \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0914\u0930 \u0926\u0942\u0938\u0930\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0905\u0935\u0938\u094d\u0925\u093e \u0938\u0947\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0909\u0938 \u091a\u0940\u091c\u093c \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0939\u092e\u0947\u0902 \u0917\u0924\u093f \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u092c\u0926\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u091c\u094b\u0921\u093c\u0928\u093e (\u092f\u093e \u0918\u091f\u093e\u0928\u093e) \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 \u0939\u092e <strong>\u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    E_{cin} &amp; \\displaystyle = \\frac{1}{2}m\\|\\vec{v}\\|^2 &amp; (5)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u0914\u0930 \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    W &amp; = \\Delta E_{cin} &amp;  (6)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u092c\u093e\u0924 <strong>\u091c\u0940\u0935\u093f\u0924 \u092c\u0932 \u092a\u094d\u0930\u092e\u0947\u092f<\/strong> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u093e\u0928\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ddddff;\">\n<h4 style=\"color: #800000;\">\u0905\u092d\u094d\u092f\u093e\u0938<\/h4>\n<p style=\"text-align:justify;\"><strong>a) <a href=\"https:\/\/www.youtube.com\/watch?v=_q-5C4FQOaU&amp;t=1148s\" target=\"_blank\" rel=\"noopener\">\u090f\u0915 \u0935\u093e\u0939\u0928 \u091c\u0948\u0938\u0947 \u0915\u093f KIA Rio 5 \u0915\u093e \u0935\u091c\u0928<\/a><\/strong> \u0932\u0917\u092d\u0917 1,580 \u0915\u093f\u0932\u094b\u0917\u094d\u0930\u093e\u092e \u0939\u0948\u0964 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u0906\u092a \u0907\u0938 \u0935\u093e\u0939\u0928 \u0915\u094b \u0936\u0939\u0930 \u092e\u0947\u0902 50 \u0915\u093f\u092e\u0940\/\u0918\u0902\u091f\u093e \u0915\u0940 \u092e\u0927\u094d\u092f\u092e \u0917\u0924\u093f \u0938\u0947 \u091a\u0932\u093e \u0930\u0939\u0947 \u0939\u0948\u0902 \u0914\u0930 \u090f\u0915 \u0932\u093e\u0932 \u092c\u0924\u094d\u0924\u0940 \u0938\u0947 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902\u0964 \u0930\u0941\u0915\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0935\u093e\u0939\u0928 \u0915\u094b \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0938\u093f\u0938\u094d\u091f\u092e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0909\u0938 \u090a\u0930\u094d\u091c\u093e \u0915\u094b \u092b\u0948\u0932\u093e\u0928\u093e \u0939\u094b\u0917\u093e\u0964 \u092b\u093f\u0930, \u0917\u0924\u093f \u0915\u094b \u092a\u0941\u0928\u0903 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0907\u0938\u0947 \u0908\u0902\u0927\u0928 \u0938\u0947 \u090a\u0930\u094d\u091c\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0940 \u0939\u094b\u0917\u0940\u0964 \u092f\u0926\u093f \u092c\u0924\u094d\u0924\u0940 \u0939\u0930\u0940 \u0939\u094b\u0924\u0940, \u0924\u094b \u092c\u094d\u0930\u0947\u0915 \u0932\u0917\u093e\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u090a\u0930\u094d\u091c\u093e \u0915\u0940 \u092c\u091a\u0924 \u0939\u094b\u0924\u0940\u0964 \u092f\u0926\u093f \u092c\u0924\u094d\u0924\u0940 \u0939\u0930\u0940 \u0939\u0948 \u0924\u094b \u092c\u091a\u093e\u0908 \u0917\u0908 \u090a\u0930\u094d\u091c\u093e \u0915\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0964<\/p>\n<p>    <strong>b)<\/strong> \u092a\u093f\u091b\u0932\u0947 \u0916\u0902\u0921 \u0915\u0947 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u094b \u0926\u094b\u0939\u0930\u093e\u090f\u0902, \u0932\u0947\u0915\u093f\u0928 \u0905\u092c \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0906\u092a \u0915\u092e \u092e\u0927\u094d\u092f\u092e \u0917\u0924\u093f 70 \u0915\u093f\u092e\u0940\/\u0918\u0902\u091f\u093e \u092a\u0930 \u091a\u0932\u093e \u0930\u0939\u0947 \u0939\u0948\u0902\u0964 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u090a\u0930\u094d\u091c\u093e \u0935\u094d\u092f\u092f \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0936\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0947\u0902\u0964<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/dGK-y2Pqu74\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"12\"><\/a><\/p>\n<h3>\u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0914\u0930 \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940<\/h3>\n<p style=\"text-align:justify;\">\u092e\u094b\u091f\u0930 \u091a\u093e\u0932\u0915\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u090f\u0915 \u092c\u0939\u0941\u0924 \u0939\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0917\u0932\u0924\u0940 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0935\u0947 \u092f\u0939 \u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940 \u0938\u0940\u0927\u0947 \u0917\u0924\u093f \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948: \u092f\u0926\u093f \u0939\u092e \u0917\u0924\u093f \u0915\u094b \u0926\u094b\u0917\u0941\u0928\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940 \u092d\u0940 \u0926\u094b\u0917\u0941\u0928\u0940 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0916\u0902\u0921 \u092e\u0947\u0902 \u0939\u092e \u0907\u0938 \u0927\u093e\u0930\u0923\u093e \u0915\u0947 \u092a\u0940\u091b\u0947 \u0915\u0940 \u0917\u0932\u0924\u0940 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940 \u0917\u0924\u093f \u0915\u0947 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGK-y2Pqu74&amp;t=113s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u092c\u094d\u0932\u0949\u0915 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u0939\u0948<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">v_i\\hat{x}<\/span> \u0938\u0947 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0924\u0932 \u092a\u0930 \u091a\u0932 \u0930\u0939\u093e \u0939\u0948 \u0914\u0930 \u091c\u0939\u093e\u0902 \u090f\u0915 \u0917\u0924\u093f\u091c \u0918\u0930\u094d\u0937\u0923 \u0917\u0941\u0923\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c.<\/span> \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u0939\u092e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u090f\u0915 \u0918\u0930\u094d\u0937\u0923 \u092c\u0932 \u0939\u0948 \u091c\u094b \u0917\u0924\u093f \u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{roce}=-\\mu_c mg\\hat{x}<\/span> \u091c\u094b \u0924\u092c \u0924\u0915 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0947\u0917\u093e \u091c\u092c \u0924\u0915 \u0936\u0930\u0940\u0930 \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">x_{fre}.<\/span> \u0915\u094b \u092a\u093e\u0930 \u0915\u0930 \u0915\u0947 \u0930\u0941\u0915 \u0928\u0939\u0940\u0902 \u091c\u093e\u0924\u093e\u0964 \u0907\u0938 \u092c\u0932 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u090f \u0917\u090f \u0915\u093e\u0930\u094d\u092f \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n    \\displaystyle W_{roce}= \\int_{0}^{x_{fre}} \\vec{F}_{roce} \\cdot d\\vec{l} = \\int_{0}^{x_{fre}} -\\mu_c mg dx = -\\mu_cmgx_{fre}\n\n    <\/span>\n<p style=\"text-align:justify;\">\u0926\u0942\u0938\u0930\u0940 \u0913\u0930, \u090f\u0915 \u0936\u0930\u0940\u0930 \u0915\u0940 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">v_i<\/span> \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 \u0917\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">v_f=0<\/span> \u092a\u0930 \u0930\u0941\u0915 \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Delta E_{cin}= \\frac{1}{2}m (\\underbrace{\\color{red}{v_f^2}}_{= 0} - v_i^2) = - \\frac{1}{2}mv_i^2\n\n    <\/span>\n<p style=\"text-align:justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093f \u092f\u0926\u093f \u0938\u093e\u0930\u0940 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u094b \u0918\u0930\u094d\u0937\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u092b\u0948\u0932\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0924\u0915 \u0915\u093f \u0936\u0930\u0940\u0930 \u0915\u094b \u0936\u093e\u0902\u0924\u093f \u092e\u0947\u0902 \u0932\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u092c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\begin{array}{rrl}\n\n    &amp; W_{roce} &amp; \\displaystyle = \\Delta E_{cin} \\\\ \\\\\n\n \\equiv   &amp; -\\mu_cmg x_{fre} &amp; \\displaystyle = - \\frac{1}{2}mv_i^2 \\\\ \\\\\n\n \\equiv   &amp; x_{fre} &amp; = \\frac{1}{2} \\frac{v_i^2}{\\mu_c g}\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">\u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0935\u0939 \u092e\u093f\u0932\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0947 \u0939\u092e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0925\u0947, \u0915\u093f \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940 \u0917\u0924\u093f \u0915\u0947 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ddddff;\">\n<h4 style=\"color: #800000;\">\u0905\u092d\u094d\u092f\u093e\u0938<\/h4>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGK-y2Pqu74&amp;t=510s\" target=\"_blank\" rel=\"noopener\"><strong>\u090f\u0915 300[kg] \u0915\u093e \u092c\u094d\u0932\u0949\u0915<\/strong><\/a> 15[km\/h] \u0915\u0940 \u0917\u0924\u093f \u0938\u0947 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0924\u0932 \u092a\u0930 \u091a\u0932\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0924\u0932 \u0914\u0930 \u092c\u094d\u0932\u0949\u0915 \u0915\u0947 \u092c\u0940\u091a \u090f\u0915 \u0917\u0924\u093f\u091c \u0918\u0930\u094d\u0937\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c=0,67.<\/span> \u0939\u0948, \u0924\u094b \u0909\u0938 \u0926\u0942\u0930\u0940 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902 \u091c\u094b \u092c\u094d\u0932\u0949\u0915 \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0930\u0941\u0915\u0928\u0947 \u0924\u0915 \u0924\u092f \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/GXxkhk00quw\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/h2>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=GXxkhk00quw&amp;t=6s\" target=\"_blank\" rel=\"noopener\"><strong>\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u0939\u0948<\/strong><\/a> \u091c\u093f\u0938\u0915\u093e \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0939\u0948 \u091c\u094b \u090a\u0902\u091a\u093e\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">h_i<\/span> \u0938\u0947 \u0905\u0902\u0924\u093f\u092e \u090a\u0902\u091a\u093e\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">h_f<\/span> \u0924\u0915 \u0917\u093f\u0930\u0924\u0940 \u0939\u0948 (\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">h_f \\leq h_i<\/span> )\u0964 \u0924\u092c \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u092c\u0932 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0915\u093e\u0930\u094d\u092f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle W_g = \\int_{h_i}^{h_f} \\vec{F}_g \\cdot d\\vec{l} = \\int_{h_i}^{h_f} -mgdz = -mg(h_f - h_i)<\/span>\n<p style=\"text-align:justify;\">\u0907\u0938\u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092f\u0926\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u090a\u0902\u091a\u093e\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">h_i = h<\/span> \u0939\u0948 \u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u090a\u0902\u091a\u093e\u0908 \u091c\u092e\u0940\u0928 \u092a\u0930 \u0939\u0948 <span class=\"katex-eq\" data-katex-display=\"false\">h_f = 0<\/span>, \u0924\u094b:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle W_g = -mg(0 - h) = mgh<\/span>\n<p style=\"text-align:justify;\">\u0907\u0938\u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u091c\u092c \u0915\u094b\u0908 \u0935\u0938\u094d\u0924\u0941 \u090a\u0902\u091a\u093e\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> \u0938\u0947 \u0917\u093f\u0930\u0924\u0940 \u0939\u0948, \u0924\u094b \u0907\u0938\u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 \u091c\u0941\u0921\u093c\u0940 \u090a\u0930\u094d\u091c\u093e \u0928\u093f\u0915\u0932\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u090a\u0930\u094d\u091c\u093e \u0915\u094b \u0939\u092e <strong>\u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\begin{array}{rr}{E_{pot} = mgh} &amp; (7)\\end{array}<\/span>\n<p><a name=\"21\"><\/a><\/p>\n<h3>\u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0914\u0930 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0917\u093f\u0930\u093e\u0935\u091f<\/h3>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=GXxkhk00quw&amp;t=329s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u092f\u093e\u0926 \u0915\u0930\u0947\u0902<\/strong><\/a>\u0964 \u0905\u092c \u0939\u092e\u0928\u0947 \u091c\u094b \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u0914\u0930 \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u092f\u093e \u0939\u0948, \u0909\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0940 \u0917\u0924\u093f \u0915\u094b \u0905\u092c \u090f\u0915 \u092c\u0939\u0941\u0924 \u0939\u0940 \u0938\u0930\u0932 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0938\u093e\u0925 \u092a\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u090a\u0930\u094d\u091c\u093e \u090f\u0915 \u0914\u0930 \u092d\u094c\u0924\u093f\u0915 \u092e\u093e\u0924\u094d\u0930\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u0902\u0930\u0915\u094d\u0937\u093f\u0924 \u0939\u094b\u0928\u0947 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948; \u0905\u0930\u094d\u0925\u093e\u0924\u094d, \u0907\u0938\u0947 \u0928 \u0924\u094b \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0928 \u0939\u0940 \u0928\u0937\u094d\u091f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0915\u0947\u0935\u0932 \u0930\u0942\u092a\u093e\u0902\u0924\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u091c\u092c \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u091c\u092e\u0940\u0928 \u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> \u0915\u0940 \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u092c \u092f\u0939 \u0917\u0941\u0930\u0941\u0924\u094d\u0935\u093e\u0915\u0930\u094d\u0937\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0917\u093f\u0930\u0915\u0930 \u091c\u092e\u0940\u0928 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0924\u0940 \u0939\u0948, \u0924\u094b \u0907\u0938\u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e \u0917\u093e\u092f\u092c \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940, \u092c\u0932\u094d\u0915\u093f \u0926\u0942\u0938\u0930\u0940 \u0930\u0942\u092a \u0915\u0940 \u090a\u0930\u094d\u091c\u093e \u092e\u0947\u0902 \u092c\u0926\u0932 \u091c\u093e\u0924\u0940 \u0939\u0948: \u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e, \u0907\u0938\u0932\u093f\u090f:<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n    E_{pot,inicial} &amp; = E_{cin, final} \\\\ \\\\ mgh &amp;\\displaystyle = \\frac{1}{2}mv^2 \\\\ \\\\ v^2 &amp; = 2gh \\\\ \\\\ v&amp; =\\sqrt{2gh}\\end{array}<\/span>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ddddff;\">\n<h4 style=\"color: #800000;\">\u0905\u092d\u094d\u092f\u093e\u0938<\/h4>\n<p>    <a href=\"https:\/\/www.youtube.com\/watch?v=GXxkhk00quw&amp;t=443s\" target=\"_blank\" rel=\"noopener\"><strong>\u090f\u0915 \u0930\u094b\u0932\u0930 \u0915\u094b\u0938\u094d\u091f\u0930 \u0915\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092c\u093f\u0902\u0926\u0941<\/strong><\/a> \u091c\u092e\u0940\u0928 \u0938\u0947 150[m] \u0915\u0940 \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u0939\u0948\u0964 \u092f\u0926\u093f \u0917\u093e\u0921\u093c\u0940 \u092c\u093f\u0928\u093e \u0918\u0930\u094d\u0937\u0923 \u0915\u0947 \u0930\u094b\u0932\u0930 \u0915\u094b\u0938\u094d\u091f\u0930 \u0915\u0947 \u0930\u0947\u0932 \u092a\u0930 \u091a\u0932\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0935\u093f\u0936\u094d\u0930\u093e\u092e \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b \u091c\u092c \u092f\u0939 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u090a\u0902\u091a\u093e\u0908 \u092a\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0924\u094b \u0909\u0938\u0915\u0940 \u0917\u0924\u093f \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:<\/p>\n<p>    <strong>a)<\/strong> \u091c\u092e\u0940\u0928 \u0938\u0947 90[m] \u0915\u0940 \u090a\u0902\u091a\u093e\u0908\u0964<\/p>\n<p>    <strong>b)<\/strong> \u091c\u092e\u0940\u0928 \u0938\u0947 50[m] \u0915\u0940 \u090a\u0902\u091a\u093e\u0908\u0964<\/p>\n<p>    <strong>c)<\/strong> \u091c\u092e\u0940\u0928 \u0938\u0947 10[m] \u0915\u0940 \u090a\u0902\u091a\u093e\u0908\u0964<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e \u0938\u093e\u0930\u093e\u0902\u0936: \u0939\u092e \u0907\u0938 \u0915\u0915\u094d\u0937\u093e\u0913\u0902 \u0915\u0940 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0915\u094b \u0915\u093e\u0930\u094d\u092f, \u090a\u0930\u094d\u091c\u093e, \u0914\u0930 \u0909\u0928\u0915\u0940 \u0915\u0941\u091b \u0930\u0942\u092a\u094b\u0902: \u0917\u0924\u093f\u091c \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f\u091c \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u0930\u094d\u092a\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0907\u0928 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u094b\u0902 \u0938\u0947 \u0939\u092e \u090f\u0915 \u091a\u0932 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u092c\u094d\u0930\u0947\u0915\u093f\u0902\u0917 \u0926\u0942\u0930\u0940 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0917\u0924\u093f \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0930\u0941\u0915\u0928\u0947 \u0924\u0915 \u091a\u0932\u0924\u0940 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28589,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":9,"footnotes":""},"categories":[643,659],"tags":[],"class_list":["post-28596","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-643","category-659"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u090a\u0930\u094d\u091c\u093e \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948\u0902: \u091c\u092c \u0915\u094b\u0908 \u092c\u0932 \u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u094b \u0939\u093f\u0932\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0947 \u090a\u0930\u094d\u091c\u093e \u0926\u0947\u0924\u093e \u0939\u0948, \u0924\u094b \u0909\u0938\u0947 \u0915\u093e\u0930\u094d\u092f \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u090a\u0930\u094d\u091c\u093e \u0935\u0939 \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u094b \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u094b \u0939\u093f\u0932\u0928\u0947 \u092f\u093e \u092c\u0926\u0932\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0940 \u0939\u0948, \u091c\u0948\u0938\u0947 \u091c\u092c \u0915\u094b\u0908 \u0935\u0938\u094d\u0924\u0941 \u0917\u0924\u093f \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948 (\u0917\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e) \u092f\u093e \u090a\u0901\u091a\u093e\u0908 \u092a\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948 (\u0938\u094d\u0925\u093f\u0924\u093f\u091c \u090a\u0930\u094d\u091c\u093e)\u0964 \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902, \u0915\u093e\u0930\u094d\u092f \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u094b \u0939\u093f\u0932\u093e\u0928\u0947 \u092f\u093e \u092c\u0926\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u093e \u0939\u0948\u0964\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/hi\/\u0915\u093e\u0930\u094d\u092f-\u0914\u0930-\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915-\u090a\u0930\u094d\u091c\u093e\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u090a\u0930\u094d\u091c\u093e\" \/>\n<meta property=\"og:description\" content=\"\u0915\u093e\u0930\u094d\u092f \u0914\u0930 \u090a\u0930\u094d\u091c\u093e \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948\u0902: \u091c\u092c \u0915\u094b\u0908 \u092c\u0932 \u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u094b \u0939\u093f\u0932\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0947 \u090a\u0930\u094d\u091c\u093e \u0926\u0947\u0924\u093e \u0939\u0948, \u0924\u094b \u0909\u0938\u0947 \u0915\u093e\u0930\u094d\u092f \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u090a\u0930\u094d\u091c\u093e \u0935\u0939 \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u094b \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u094b \u0939\u093f\u0932\u0928\u0947 \u092f\u093e \u092c\u0926\u0932\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0940 \u0939\u0948, \u091c\u0948\u0938\u0947 \u091c\u092c \u0915\u094b\u0908 \u0935\u0938\u094d\u0924\u0941 \u0917\u0924\u093f \u092e\u0947\u0902 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