Mechanical Measurements HW3 Solution

Mechanical Measurements HW3 Solution - PROBLEM 11.6 KNOWN:...

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PROBLEM 11.6 KNOWN: A Wheatstone bridge with all resistances initially equal to 100 . The maximum power through R 1 is 0.25 W. FIND: Maximum applied voltage Bridge sensitivity ASSUMPTIONS: Infinite meter resistance SOLUTION: From the circuit shown below ( 29 1 1 22 12 i i i R i RE iii iR += == But we know power, P , is given by 2 P iR = , and 0.25 W 0.05 A 100 i At node A 13 2 0.1 A ii i ii =+ ( 29( 29 where is the equivalent bridge resistance so 0.1 A 100 10 V i i BB i E i RR E = = Ω= The bridge sensitivity is defined as 0 1 B E K R d d = and for a bridge with all resistances initially equal and assuming d = ( 29 0 10 V 100 2.5 V/ 4 400 i E ER d d = ≈Ω
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PROBLEM 11.8 KNOWN: A strain gauge has a nominal resistance of 350 , and GF = 1.8, and senses axial strain. The gauge is mounted on a 1 cm 2 aluminum rod ( E m = 70 GPa) E o = 1 mV, E i = 5 V. FIND: Applied load, assuming uniaxial tension SOLUTION: For an equal arm bridge, from (11.14) ( 29 ( 29 ( 29 ( 29 0 0.001 4 2 5 42 i R R RR E E R R dd d == ++ and 0.0008 0.28 R = =Ω Since 0.00044 R R GF dee = ⋅= and with ( 29( 29 0.0004 4 70 GPa 0.0308 GPa m m E E s e se s = = = To find the applied force, F N ( 29 2 2 52 c 5 29 A 1 1 0 m 7.85 4 1 0 m 4 7.85 0 m 0.030 8 10 Pa N c N F A F p s -- - = = × = ×× and since 2
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This homework help was uploaded on 04/04/2008 for the course 650 350 taught by Professor Shan during the Spring '08 term at Rutgers.

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Mechanical Measurements HW3 Solution - PROBLEM 11.6 KNOWN:...

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