EX9.2-Car_Crash

# EX9.2-Car_Crash - j m v m t F A A A B A ˆ 20 2-= ∆-i m v...

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Lesson 9 Example 9.2 Car Crash Just a little Icy

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3/208 Car B weighs 3200 lb and travels west at 30 mph. Car A weighs 3400 lbs and travels north at 20 mph. Upon crashing, they travel as one and move together. What direction do they go, and how fast directly after the impact? What is your first step? EX9.2 Car Crash Solution: Problem Type: Find: Given: W carA =3400 lb, W carB =3200 lb , v B =30mph, v A =20 mph What is the velocity of the combined cars after impace Kinetics: Impulse-Momentum Reflection: Magnitudes seem reasonable for just after the collision. Direction of to the left and up seems correct as well. Draw FBD to Identify forces during impact Write Impulse –Momentum Equation 2 1 t t dt F d 1 2 v m v m d d - = F A-B F B-A y x Let’s apply the impulse momentum equation for each car- we can model the impulse as an average Force time a delta T . Write out the vector equation for each one.
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Unformatted text preview: j m v m t F A A A B A ˆ 20 2-= ∆-i m v m t F B B B A B ˆ ) 30 ( 1--= ∆-What is true about F A-B and F B-A ? They are equal and opposite. Now, substitute F B-A = -F A-B and add the two equations above together. j m v m t F A A A B A ˆ 20 2-= ∆-i m v m t F B B B B A ˆ ) 30 ( 1--= ∆--j m i m v m v m A B B B A A ˆ 20 ˆ ) 30 ( 2 2---+ = This is essentially the derivation for Eq 3/28 What is true about v A2 and v B2 ? They are the same so call it v 2 . Substitute and solve j m i m v m m A B B A ˆ 20 ˆ ) 30 ( ) ( 2---+ = ) ( ˆ 3 . 10 ˆ 55 . 14 ) ( ˆ 20 ˆ ) 30 ( 2 mph j i m m j m i m v B A A B +-= + +-= Careful with units- you would need to divide the weights by g, but they would end up cancelling in the equation. Same for the mph conversion....
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EX9.2-Car_Crash - j m v m t F A A A B A ˆ 20 2-= ∆-i m v...

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