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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