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Tuesday, August 7, 2012

Final 14 - Pushing A Car


Given:

  • \mbox{A car is being pushed by three equal force with one on each side at 30 degrees and one in the rear.}
  • \mbox{The 1000 kg car is being accelerated at 0.5 m/s/s by  the efforts of these three.}  

Question:

  • \mbox{What force are each exerting on the car?}

Rationale:

  • F = F_1 = F_2 = F_3
  • F_y = F \cos\alpha \; \mbox{(and there are two of these forces)}
    • F_{total} = F + (2 F \cos\alpha)  
  • F_{car} = m a = F + (2 F \cos\alpha)  
  • F (1+(2 \sin\alpha) = m a
  • F = \dfrac{( m a)}{(1+(2 \cos\alpha)}

Calculate:

  • F = \dfrac{(100 * .5)}{(1 + (2 * .866025)} = \dfrac{500}{2.73205} = 183.012756 \approx 183

References:

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