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Application of Fluid Dynamics and Energy Conservation in Mechanical Systems

An analysis of fluid dynamics principles and energy conservation in mechanical engineering systems.

Anna Wilson
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Application of Fluid Dynamics and Energy Conservation in Mechanical SystemsA child’s race track is shown (not to scale) in the figure above. A toy car with a massof 24.3 g is released from rest at the starting position. In the figure R = 19.1 cmandh = 63.9 cm.What is the initial gravitational potential energy of the car?______Jπ‘ˆ=π‘šπ‘”β„Ž==>π‘ˆ=(24.31000)βˆ—(9.8)βˆ—(0.639)==>π‘ˆ=0.15217==>π‘ˆ=𝟎.πŸπŸ“πŸπ‘±------------------------------------------------------------------------------------What is the speed of the car at the top of the loop?______m/sconservation of energy:π‘“π‘–π‘›π‘Žπ‘™π‘’π‘›π‘’π‘Ÿπ‘”π‘¦=π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™π‘’π‘›π‘’π‘Ÿπ‘”π‘¦π‘šπ‘”(2𝑅)+(12)π‘šπ‘£2=π‘šπ‘”β„Ž==>𝑔(2𝑅)+(12)𝑣2=π‘”β„Ž==>(12)𝑣2=π‘”β„Žβˆ’π‘”(2𝑅)==>𝑣2=2𝑔(β„Žβˆ’2𝑅)==>𝑣=√2𝑔(β„Žβˆ’2𝑅)==>𝑣=√2βˆ—(9.8)βˆ—(0.639βˆ’2βˆ—0.191)==>𝑣=2.2444π‘š/𝑠==>𝒗=𝟐.πŸπŸ’π’Ž/𝒔------------------------------------------------------------------------------------What is the magnitude of the acceleration of the car at the top of the loop?__m/s2

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