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kogti
8 days ago
10

A car has a crumple zone that is 0.80 m (80 cm) long. In this car, the distance from the dummy to the steering wheel is 0.50 m.

The car has a mass of 1,600 kg and the dummy has a mass of 75 kg. At the time of the crash, the car has a speed of 18 m/s. Based on the work-energy theorem, what is the smallest possible force that the dummy could experience during the crash
Physics
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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
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Answer:

\int\limits^2_0 {} \, \int\limits^{5\pi}_0 {F(S(u,v)).N} \,dvdu ≈ 3077.34

Explanation:

To calculate the flux of F (vector field) across surface S, where

F(x,y,z) = y i − x j + z^{2} k

and S(u,v) = u cos v i + u sin v j + v k, 0 ≤ u ≤ 2, 0 ≤ v ≤ 5π

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\int\limits^2_0 {} \, \int\limits^{5\pi}_0 {F(S(u,v)).N} \,dvdu

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The normal vector N is computed as

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Where:

S_{u} = =

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N = < cos v, sin v, 0 > X <- u sin v, u cos v, 2v

N = < 2v sin v, -2v cos v, u >

F(S(u,v)).N = < u sin v, -u cos v, v^{2}>. < 2v sin v, -2v cos v, u >

F(S(u,v)).N = 2uv + uv^{2}

Thus

\int\limits^2_0 {} \, \int\limits^{5\pi}_0 {2uv}+u v^{2}\,dvdu ≈ 3077.34

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