Kinetisk energi for en partikelOpgaven er en kommentar til opgave 7 fra semesteruge 1, for\303\245ret 2016, store dag.Formlen for kinetisk energi lyder, n\303\245r der regnes 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er alts\303\245 Taylor-polynomiet af 3. grad til den relativistiske formel.Hvor god er s\303\245 approksimationen?Som man kan se af Taylor-udviklingen ovenfor, s\303\245 er alle led positive, dvs. fejlen vokser n\303\245r LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= vokser.Antag at 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, dvs. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJiZsZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSQwLjFGJ0Y5LUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZXLUYsNiVRImNGJ0YvRjJGOQ==Den maksimale fejl findes derfor, n\303\245r LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJDAuMUYnRjktRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlctRiw2JVEiY0YnRi9GMkY5Fejlen skal nu beregnes:PkkvTWF4RmVqbEFic29sdXRHNiIsJi1JJUVraW5HRiQ2IywkSSJjR0YkJCIiIiEiIkYsKiYmSSJtR0YkNiMiIiFGLC1JIl5HJSpwcm90ZWN0ZWRHNiRGKSIiI0YsI0YtRjc=PkkwTWF4ZmVqbFByb2NlbnQxRzYiLCQqJkkvTWF4RmVqbEFic29sdXRHRiQiIiItSSVFa2luR0YkNiMsJEkiY0dGJCRGKCEiIkYvIiQrIg==PkkwTWF4ZmVqbFByb2NlbnQyRzYiLCQqJkkvTWF4RmVqbEFic29sdXRHRiQiIiItSSIvRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComJkkibUdGJDYjIiIhRigtSSJeR0YsNiQsJEkiY0dGJCRGKCEiIiIiI0YoI0YoRjxGKCIkKyI=Konklusion: N\303\245r 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 af LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= , vil man maksimalt lave en fejl p\303\245 godt LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KS1JI21uR0YkNiZRIjNGJy8lK2JhY2tncm91bmRHUS5bMjA0LDI1NSwyNTVdRicvJSdvcGFxdWVHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNictRi82JlEiNEYnRjJGNUY4LyUnaXRhbGljR0Y3RjJGNS9GOVEnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGMi1JI21pR0YkNidRIiVGJ0ZARjJGNUZCRjJGNUY4 , hvis man anvender den klassiske formel for kinetisk energi (frem for den relativistiske).NB: Fejlens st\303\270rrelse i procent er uafh\303\246ngig af massen.