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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.

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    Application of Fluid Dynamics and Energy Conservation in Mechanical Systems, page 1Application 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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    Application of Fluid Dynamics and Energy Conservation in Mechanical Systems, page 2

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