Quiz06_13solutions

Quiz06_13solutions - Physics 221 Quiz 6 Name Section Spring...

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Physics’22 1’ Quiz’ 6’ Spring’2013 ’ Name’&’Section’’’’ Quiz 6A A’ 1.00-kg’ ball’ is’pushed’against’a’spring’with’negligible’mass’and’force’constant’k ’ =’ 49.0’ N/m,’ compressing’it’0. 500’ m.’ When’the’block’is’released ’ from’rest ,’it ’ leaves’the’end’of’the’spring’and ’ moves’ along’a’frictionless,’horizontal’surface’and’th en’ goes’ up’ along’ a’frictionless’circular’track’(1/4’circle ’ from’ A’to’B ,’radius’ R’ =’ 0.500’ m).’ (a) Is’mechanical’energy’conserved’when’it’is’moving’on’the’track?’What’is’the’value’of’the’ mechanical’energy’of’the’ball? (b) What’is’the’centripetal’acceleration’of’the’ ball’when’it’ begins’ to’ move’ along’ the’circular’track ’ (Position’A) ?’ (c) What’is’the’ highest’point ’ the’ball’ can’ reach?’ Solution:’ (a) Yes,’m echanical’energy’is’conserved: 22 11 (49 / )(0.5 ) 6.125 6.13 el EE kx Nm m J J == Δ = = = (b) Mechanical’energy’is’conserved’here: el k = ,’ m v Δ = Centripetal’acceleration’is: ’ 2 / avR = Then’ 2 / / (49 / )(0.5 ) / (1 ) / (0.5 ) 24.5 / akxmR k g m ms = Δ = = ’ ’ (c) The’velocity’of’the’ball’at’highest’point’is’0. Mechanical’energy’is’conserved’here: kp = ,’ 2 1 2 kx m g h Δ = Then’ 2 / 2 (49 / )(0.5 ) / 2 / (1 ) / (9.8 / ) 0.625 hkx m g k g m = Δ = =
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