Questões de Física · INEP (ENEM)

FísicaDinâmica da rotação e momento angularINEP (ENEM) 2014

ENADE

Questão de Física

1 ∂v ƉĂƌĐŝĂůĚŽǀŽůƵŵĞĞƐƉĞĐşĮĐŽĞŵƌĞůĂĕĆŽăƚĞŵƉĞƌĂƚƵƌĂ͕ĚĞĂĐŽƌĚŽ ĐŽŵĂĞƋƵĂĕĆŽγ = . v ∂T P ŽŶƐŝĚĞƌĞ ĚƵĂƐ ƉĞĕĂƐ ;ƚƌŽŶĐŽƐ ĚĞ ĐŽŶĞ ŽĐŽƐ ĚĞ ŵĂƚĞƌŝĂŝƐ ĚŝĨĞƌĞŶƚĞƐͿ ƌŝŐŝĚĂŵĞŶƚĞ ƉƌĞƐĂƐ ƵŵĂ ĚĞŶƚƌŽ ĚĂ

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EĞƐƐĞĐŽŶƚĞdžƚŽ͕ĨĂĕĂŽƋƵĞƐĞƉĞĚĞŶŽƐŝƚĞŶƐĂƐĞŐƵŝƌ͘ ĂͿ džƉůŝƋƵĞƵŵĂĨŽƌŵĂĚĞƐĞƉĂƌĂƌĞƐƐĂƐĚƵĂƐƉĞĕĂƐŵĞƚĄůŝĐĂƐƵƟůŝnjĂŶĚŽŽĐŽŶĐĞŝƚŽĚĞĚŝůĂƚĂĕĆŽǀŽůƵŵĠƚƌŝĐĂ͘ ;ǀĂůŽƌ͗ϱ͕ϬƉŽŶƚŽƐͿ ďͿ /ŶĚŝƋƵĞĂŽŵĞŶŽƐĚƵĂƐǀĂƌŝĄǀĞŝƐ;ŽƵĐŽŶĚŝĕƁĞƐͿĚĂƐƋƵĂŝƐŽƐĞƵŵĠƚŽĚŽƉŽĚĞƌĄĚĞƉĞŶĚĞƌ͘;ǀĂůŽƌ͗ϱ͕ϬƉŽŶƚŽƐͿ 1 2 ϯ 4 5 6 7 ϴ 9 10 11 12 ϭϯ 14 15 9 &1^/ QUESTÃO DISCURSIVA 4 KĂĐŝĚĞŶƚĞƌĂĚŝŽůſŐŝĐŽĚĞ'ŽŝąŶŝĂ͕ĂŵƉůĂŵĞŶƚĞĐŽŶŚĞĐŝĚŽĐŽŵŽĂĐ ŝĚĞŶƚĞĐŽŵŽĠƐŝŽͲϭϯϳ͕ĨŽŝƵŵŐƌĂǀĞ ĞƉŝƐſĚŝŽ ĚĞ ĐŽŶƚĂŵŝŶĂĕĆŽ ƉŽƌ ƌĂĚŝĂƟǀŝĚĂĚĞ ŽĐŽƌƌŝĚŽ ŶŽ ƌĂƐŝů͘ ĐŽŶƚĂŵŝŶĂĕĆŽ ƚĞǀĞ ŝŶşĐŝŽ Ğŵ ϭϯ ĚĞ ƐĞƚĞŵďƌŽĚĞϭϵϴϳ͕ƋƵĂŶĚŽƵŵĂƉĂƌĞůŚŽƵƟůŝnjĂĚŽĞŵƌĂĚŝŽƚĞƌĂƉŝĂƐ ĨŽŝĞŶĐŽŶƚƌĂĚŽĚĞŶƚƌŽĚĞƵŵĂĐůşŶŝĐĂ ĂďĂŶĚŽŶĂĚĂ͕ŶŽĐĞŶƚƌŽĚĞ'ŽŝąŶŝĂ͘KŝŶƐƚƌƵŵĞŶƚŽĨŽŝĞŶĐŽŶƚƌĂĚŽ ƉŽƌĐĂƚĂĚŽƌĞƐĚĞƵŵĨĞƌƌŽǀĞůŚŽĚŽůŽĐĂů͕ ƋƵĞ ĞŶƚĞŶĚĞƌĂŵ ƚƌĂƚĂƌͲƐĞ ĚĞ ƐƵĐĂƚĂ͘ &Žŝ ĚĞƐŵŽŶƚĂĚŽ Ğ ƌĞƉĂƐƐĂĚŽ ƉĂƌĂ ƚĞƌĐĞŝƌŽƐ͕ ŐĞƌĂŶĚŽ Ƶŵ ƌĂƐƚƌŽ ĚĞ ĐŽŶƚĂŵŝŶĂĕĆŽ͕ŽƋƵĂůĂĨĞƚŽƵƐĞƌŝĂŵĞŶƚĞĂƐĂƷĚĞĚĞĐĞŶƚĞŶĂƐĚĞƉ ĞƐƐŽĂƐ͘KĂĐŝĚĞŶƚĞĐŽŵŽĠƐŝŽͲϭϯϳĨŽŝŽ ŵĂŝŽƌĂĐŝĚĞŶƚĞƌĂĚŝĂƟǀŽĚŽƌĂƐŝůĞŽŵĂŝŽƌĚŽŵƵŶĚŽŽĐŽƌƌŝĚŽĨŽƌĂĚĂƐƵƐŝŶĂƐŶƵĐůĞĂƌĞƐ͘ EŽŝŶƚĞƌŝŽƌĚĂ ĐĄƉƐƵůĂĚŽĂƉĂƌĞůŚŽĚĞƌĂĚŝŽƚĞƌĂƉŝĂ͕ŚĂǀŝĂůŽƌĞ ƚŽĚĞĠƐŝŽŶĂĨŽƌŵĂĚĞƵŵƉſ͘ ĞƌĐĂĚĞ ϭϵ͕ϮϲŐĚĞƐƐĞƉſƐĞĞƐƉĂůŚŽƵ͕ĨŽŝŵĂŶŝƉƵůĂĚŽĞĂƚĠŝŶŐĞƌŝĚŽƉŽƌ ĚŝǀĞƌƐĂƐƉĞƐƐŽĂƐ͘ƉŽƉƵůĂĕĆŽĚĞ'ŽŝąŶŝĂĨŽŝ ĞdžĂŵŝŶĂĚĂĞ͕ĚĞϭϭϮϴϬϬƉĞƐƐŽĂƐ͕ĐĞƌĐĂĚĞϮϰϵĨŽƌĂŵĐŽŶƚĂŵŝŶĂĚĂ ƐƉĞůŽĠƐŝŽ͘ WŽƌƉƌĞĐĂƵĕĆŽ͕ĨŽƌĂŵĐŽůĞƚĂĚĂƐƚŽŶĞůĂĚĂƐĚĞŵĂƚĞƌŝĂůƋƵĞƉŽĚĞƌŝ ĂŵƚĞƌƐŝĚŽĐŽŶƚĂŵŝŶĂĚĂƐƉĞůŽƉſĚĞĠƐŝŽ͘ ƐƐĞŵĂƚĞƌŝĂůĨŽŝƐĞƉĂƌĂĚŽĞŵĚŽŝƐĐŽŶƚġŝŶĞƌĞƐ͕ŽƉƌŝŵĞŝƌŽ͕ĚĞ ďĂŝdžĂĐŽŶĐĞŶƚƌĂĕĆŽĚĞŵĂƚĞƌŝĂůƌĂĚŝĂƟǀŽ͕ƋƵĞ ƉŽĚĞƐĞƌĐŽŶƐŝĚĞƌĂĚŽůŝdžŽĐŽŵƵŵ͕ĞŽƐĞŐƵŶĚŽ͕ƋƵĞĂƌŵĂnjĞŶĂŽƐŵ ĂƚĞƌŝĂŝƐĞĨĞƚŝǀĂŵĞŶƚĞƌĂĚŝĂƚŝǀŽƐ͘ ƐƚĞƐĞŐƵŶĚŽĐŽŶƚġŝŶĞƌĠƌĞǀĞƐƟĚŽĚĞƵŵĂĐĂŵĂĚĂĚĞĐŚƵŵďŽĚĞĂƉƌŽdžŝŵĂĚĂŵĞŶƚĞϭϬĐŵ͘ ŽŵďĂƐĞŶĞƐƐĂƐŝƚƵĂĕĆŽ͕ĨĂĕĂŽƋƵĞƐĞƉĞĚĞŶŽƐŝƚĞŶƐĂƐĞŐƵŝƌ͘ ĂͿ džƉůŝƋƵĞĂĚŝĨĞƌĞŶĕĂĞŶƚƌĞĐŽŶƚĂŵŝŶĂĕĆŽĞŝƌƌĂĚŝĂĕĆŽ͘;ǀĂůŽƌ͗ ϰ͕ϬƉŽŶƚŽƐͿ ďͿ ^ĂďĞͲƐĞ ƋƵĞ Ă ůĞŝ ĚĞ ĚĞĐĂŝŵĞŶƚŽ ƌĂĚŝĂƟǀŽ ĞƐƚĂďĞůĞĐĞ ƋƵĞ N = N e−t/τ ͕ Ğŵ ƋƵĞ τ Ġ Ă ǀŝĚĂ ŵĠĚŝĂ͘ 0 ŽŶƐŝĚĞƌĂŶĚŽƋƵĞŽĠƐŝŽƚĞŵƵŵĂǀŝĚĂŵĠĚŝĂĚĞϯϬĂŶŽƐ͕ĂƉƌŽdžŝŵ ĂĚĂŵĞŶƚĞ͕ĞĚĞĐĂŝĞŵŝƟŶĚŽƉĂƌơĐƵůĂƐ beta e gamma, ĞƐƟŵĞƋƵĂŶƚŽƐŐƌĂŵĂƐĚĞĠƐŝŽͲϭϯϳĚŽĂĐŝĚĞŶƚĞĚĞ'ŽŝąŶŝĂƐĞƌŝĂŵƌĂĚŝĂƟǀŽƐĂŝŶĚĂŚŽũĞ͘ ;ǀĂůŽƌ͗ϯ͕ϬƉŽŶƚŽƐͿ ĐͿ ^ĂďĞͲƐĞƋƵĞĂƐƉĂƌơĐƵůĂƐgammaĞŵŝƟĚĂƐƉĞůŽĠƐŝŽƉŽĚĞŵƐĞƌĂďƐŽƌǀŝĚĂƐƉĞůĂƉĂƌĞĚĞĚĞĐŚƵŵďŽĞ ƋƵĞŽŶƷŵĞƌŽĚĞƉĂƌơĐƵůĂƐgammaĂďƐŽƌǀŝĚĂƐĚĞƉĞŶĚĞĚĂĞƐƉĞƐƐƵƌĂĚĂĐĂŵĂĚĂĚĞĐŚƵŵďŽ͕ĚĞĂĐŽƌĚŽ ĐŽŵĂƐĞŐƵŝŶƚĞĞƋƵĂĕĆŽ͗ N = N e−x/lo ͕ĞŵƋƵĞ x ĠĂĞƐƉĞƐƐƵƌĂĚĂĐĂŵĂĚĂĚĞĐŚƵŵďŽĞl = 1cm 0 0 ĠƵŵĨĂƚŽƌĂƐƐŽĐŝĂĚŽăĂďƐŽƌĕĆŽ͘ŽŵďĂƐĞŶĞƐƐĂƐŝŶĨŽƌŵĂĕƁĞƐ͕Ğ džƉůŝƋƵĞƐĞĂĞƐƉĞƐƐƵƌĂĚĂƉĂƌĞĚĞĚŽ ĐŽŶƚġŝŶĞƌ ŽŶĚĞ ĨŽŝ ĂƌŵĂnjĞŶĂĚŽ Ž ŵĂƚĞƌŝĂů ĞĨĞƟǀĂŵĞŶƚĞ ƌĂĚŝĂƟǀŽ Ġ ƐƵĮĐŝĞŶƚĞ ƉĂƌĂ ĐŽŶƚĞƌ Ă ƌĂĚŝĂĕĆŽ e−10 gammaĚŽƐƌĞũĞŝƚŽƐ͘WĂƌĂŝƐƐŽ͕ĐŽŶƐŝĚĞƌĞƋƵĞ 10 ĠĂƉƌŽdžŝŵĂĚĂŵĞŶƚĞŝŐƵĂůĂ0, 4 ͘;ǀĂůŽƌ͗ϯ͕ϬƉŽŶƚŽƐͿ 10 &1^/ 1 2 ϯ 4 5 6 7 ϴ 9 10 11 12 ϭϯ 14 15 11 &1^/ QUESTÃO DISCURSIVA 5 hŵƉƌŽĨĞƐƐŽƌĚĞ&şƐŝĐĂĚĂĚƵĐĂĕĆŽĄƐŝĐĂĚĞĐŝĚĞƵƟůŝnjĂƌŽĂƉĂƌĂƚŽ ĂďĂŝdžŽ ŝŶĚŝĐĂĚŽ ƉĂƌĂ ĚĞƐĞŶǀŽůǀĞƌ ƵŵĂ ĂƟǀŝĚĂĚĞ ĚŝĚĄƟĐĂ ďĂƐĞĂĚĂ

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Ğŵ ĞdžƉĞƌŝŵĞŶƚŽ ĚŝĚĄƟĐŽͲĐŝĞŶơĮĐŽ͘ K ĂƐƐƵŶƚŽ Ă ƐĞƌ ƚƌĂƚĂĚŽ Ġ Ž ŵŽǀŝŵĞŶƚŽƵŶŝĨŽƌŵĞ͘WĂƌĂƚĂŶƚŽ͕ĞůĞĞƐƚĂďĞůĞĐĞƵŵƌŽƚĞŝƌŽ͕ŵĞĚŝ ĂŶƚĞ ŽƋƵĂůŽƐĂůƵŶŽƐƐĆŽŽƌŝĞŶƚĂĚŽƐĂƐĞŐƵŝƌƵŵĂƐĠƌŝĞĚĞƉĂƐƐŽƐͬŝƚ ĞŶƐ͘ /ŶŝĐŝĂůŵĞŶƚĞ͕ ŽƐ ĂůƵŶŽƐ ĚĞǀĞŵ ůĂŶĕĂƌ ƉĞƋƵĞŶĂƐ ŐŽƚĂƐ ĚĞ ĄŐƵĂ ŶĂ ƉĂƌƚĞ ĂďĞƌƚĂ ĚŽ ƚƵďŽ ĐŽŶƚĞŶĚŽ ſůĞŽ͖ Ă ƐĞŐƵŝƌ ĚĞǀĞŵ ĞƐĐŽůŚĞƌ ƵŵĂ mufa ĚĂƐŐŽƚĂƐĞƌĞĂůŝnjĂƌŵĞĚŝĚĂƐĚŽĞƐƉĂĕŽƉĞƌĐŽƌƌŝĚŽƉŽƌĞůĂ͕ďĞŵ ĐŽŵŽ ĚŽƚĞŵƉŽĚĞĐŽƌƌŝĚŽƉĂƌĂŝƐƐŽ͘ŽŵďĂƐĞŶĞƐƐĂƐŵĞĚŝĚĂƐ͕ŽƐĂůƵŶŽ Ɛ gota ĚĞǀĞŵ ĐĂůĐƵůĂƌ Ă ǀĞůŽĐŝĚĂĚĞ ŵĠĚŝĂ ĚĂ ŐŽƚĂ ŶŽ ƚƌĞĐŚŽ ĚĞ ĚĞƐĐŝĚĂ tira de papel ĐŽŶƐŝĚĞƌĂĚŽ͘ ƐƐĂ ƐĞƋƵġŶĐŝĂ ĚĞǀĞ ƐĞƌ ƌĞƉĞƟĚĂ ĂůŐƵŵĂƐ ǀĞnjĞƐ ƉĂƌĂ milimetrado óleo ƋƵĞ ĞƐƚĞũĂŵ ƚƌĞŝŶĂĚŽƐ Ă ŽƉĞƌĂƌ ĂƉƌŽƉƌŝĂĚĂŵĞŶƚĞ Ž ĐŽŶũƵŶƚŽ Ğ͕ ĂƐƐŝŵ͕ŽďƚĞƌŐŽƚĂƐĂĚĞƋƵĂĚĂƐĂŽĞdžƉĞ ƌŝŵĞŶƚŽ͕ ďĞŵĐŽŵŽƌĞĂůŝnjĂƌĂƐ ŵĞĚŝĚĂƐŶĞĐĞƐƐĄƌŝĂƐ͘hŵĂǀĞnjĂƟŶŐŝĚŽĞƐƐĞƉŽŶƚŽĚŽƚƌĞŝŶĂŵĞŶƚŽ͕ ŽƐĂůƵŶŽƐĚĞǀĞŵƐĞƌŽƌŝĞŶƚĂĚŽƐĂƌĞƉĞƟƌϭϬǀĞnjĞƐĂĞdžƉĞƌŝŵĞŶƚĂĕĆŽ͕ suporte universal ĐŽŵŐŽƚĂƐĞƋƵŝǀĂůĞŶƚĞƐ͕ƌĞƐƚƌŝŶŐŝŶĚŽĂƐŽďƐĞƌǀĂĕƁĞƐĞĂƐŵĞĚŝĚĂ ƐĂŽƐ ƚƌĞĐŚŽƐĚĂƐĚĞƐĐŝĚĂƐĞŵƋƵĞĂƐŐŽƚĂƐƌĞĂůŝnjĂŵŵŽǀŝŵĞŶƚŽƵŶŝĨŽƌŵĞ͘ ŶĂůŝƐĂŶĚŽ Ă ƐŝƚƵĂĕĆŽ ĂƉƌĞƐĞŶƚĂĚĂ ĂĐŝŵĂ͕ Ğ ƚĞŶĚŽ ƉŽƌ ďĂƐĞ ĂƐ Ɖƌ ĞŽĐƵƉĂĕƁĞƐ Ğ ĂƐ ƉƌŽƉŽƐŝĕƁĞƐ ĂƚƵĂŝƐ ĚŝƐĐƵƟĚĂƐĞƌĞŐŝƐƚƌĂĚĂƐŶŽąŵďŝƚŽĚĂWĞƐƋƵŝƐĂĞŵĚƵĐĂĕĆŽĞŵŝġŶĐŝĂƐ͕ďĞŵĐŽŵŽĞŵŶƐŝŶŽĚĞ&şƐŝĐĂ͕ ƌĞĚŝũĂƵŵƚĞdžƚŽĚŝƐƐĞƌƚĂƟǀŽĐŽŶƚĞŶĚŽƵŵĂĐƌşƟĐĂƐŽďƌĞĂĨŽƌŵĂĚĞƵƟůŝnjĂĕĆŽĚŽĞdžƉĞƌŝŵĞŶƚŽĂĚŽƚĂĚŽ ƉĞůŽƉƌŽĨĞƐƐŽƌĞƵŵĂƐƵŐĞƐƚĆŽĚĞĂůƚĞƌŶĂƟǀĂĚĞƉƌŽĐĞĚŝŵĞŶƚŽ͘;ǀ ĂůŽƌ͗ϭϬ͕ϬƉŽŶƚŽƐͿ 1 2 ϯ 4 5 6 7 ϴ 9 10 11 12 ϭϯ 14 15 12 &1^/

ĮŐƵƌĂĂďĂŝdžŽĂƉƌĞƐĞŶƚĂĞƐƋƵĞŵĂƟĐĂŵĞŶƚĞĚŽŝƐ ŵŽŵĞŶƚŽƐ ĚŽ ŵŽǀŝŵĞŶƚŽ ĚĞ Ƶŵ ĐŽƌƉŽ ƌşŐŝĚŽ ŶĂ ĨŽƌŵĂ ĚĞ Ƶŵ ĚŝƐĐŽ͕ ĐŽŵ ŵĂƐƐĂ ŵ Ğ ƌĂŝŽ͕ ƌ͕ ĚĞŶŽŵŝŶĂĚŽ ŝŽŝƀ͘ hŵ ĮŽ͕ ƉƌĞƐŽ ĂŽ ƚĞƚŽ Ğŵ ƵŵĂ ĞdžƚƌĞŵŝĚĂĚĞ͕ĠĞŶƌŽůĂĚŽŶĂďŽƌĚĂůĂƚĞƌĂůĚŽĚŝƐĐŽ͘ ŽƵƚƌĂ ĞdžƚƌĞŵŝĚĂĚĞ ĚŽ ĮŽ ĞƐƚĄ ƉƌĞƐĂ ŶĂ ďŽƌĚĂ ůĂƚĞƌĂůĚŽĚŝƐĐŽ͕ĚĞŵŽĚŽƋƵĞĞƐƚĞŶĆŽƉŽĚĞŐŝƌĂƌ ĞŵĨĂůƐŽ͘EĂƐŝƚƵĂĕĆŽ;ĂͿ͕ŽĐŽƌƉŽĞƐƚĄĞŵƌĞƉŽƵƐŽ ĞŵƐƵĂĂůƚƵƌĂŵĄdžŝŵĂ;ŚŵĂdžͿ͕ĐŽŵŽĮŽĞŶƌŽůĂĚŽ Ğŵ ƐƵĂ ďŽƌĚĂ͕ Ğ͕ ŶĂ ƐŝƚƵĂĕĆŽ ;ďͿ͕ Ž ĐŽƌƉŽ ĞƐƚĄ Ă ƵŵĂ ĂůƚƵƌĂ Ś͕ ƚĂů ƋƵĞ ŚŵĂdž х Ś х ŚŵŝŶ͕ Ğŵ ƋƵĞ ŚŵŝŶĠĂĂůƚƵƌĂŶĂƋƵĂůŽĮŽĞƐƚĂƌŝĂĐŽŵƉůĞƚĂŵĞŶƚĞ ĚĞƐĞŶƌŽůĂĚŽ͘ ŽŶƐŝĚĞƌĞ Ž ŵŽŵĞŶƚŽ ĚĞ ŝŶĠƌĐŝĂ ĚŽĐŽƌƉŽ;ĞŵƌĞůĂĕĆŽĂƵŵĞŝdžŽƉĞƌƉĞŶĚŝĐƵůĂƌĂŽ ƉůĂŶŽĚĂĮŐƵƌĂĞƋƵĞƉĂƐƐĂƉĞůŽƐĞƵĐĞŶƚƌŽŵĂƐƐĂͿ mr2/2 ŝŐƵĂůĂ .

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DĞĚŝĚĂƐĚĂĞŶĞƌŐŝĂƉŽƚĞŶĐŝĂů;WͿ͕ĞŶĞƌŐŝĂĐŝŶĠƟĐĂ ƌŽƚĂĐŝŽŶĂů ;ZͿ Ğ ĞŶĞƌŐŝĂ ĐŝŶĠƟĐĂ ƚƌĂŶƐůĂĐŝŽŶĂů ;dͿ ĨŽƌĂŵ ƌĞĂůŝnjĂĚĂƐ Ğ ŐƌĂĮĐĂĚĂƐ ;Ğŵ ƵŶŝĚĂĚĞƐ ĂƌďŝƚƌĄƌŝĂƐͿ ĂŽ ůŽŶŐŽ ĚŽ ŵŽǀŝŵĞŶƚŽ ĚĞ ĚĞƐĐŝĚĂ ĚŽ ŝŽŝƀ͕ ĚĞƐĚĞ Ă ĂůƚƵƌĂ ŵĄdžŝŵĂ ĂƚĠ ƵŵĂ ĂůƚƵƌĂ Ś͘ ŽŶƐŝĚĞƌĂŶĚŽ ƋƵĞ ŚŽƵǀĞ ĐŽŶƐĞƌǀĂĕĆŽ ĚĂ ĞŶĞƌŐŝĂ ŵĞĐąŶŝĐĂ ƚŽƚĂů͕ ĐŽŶĐůƵŝͲƐĞ ƋƵĞ ƐĆŽ ĐŽŶƐŝƐƚĞŶƚĞƐ ĐŽŵŽƐƌĞƐƵůƚĂĚŽƐĞƐƉĞƌĂĚŽƐƚĞŽƌŝĐĂŵĞŶƚĞĂƋƵĞůĞƐ ĂƉƌĞƐĞŶƚĂĚŽƐŶŽŐƌĄĮĐŽ

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