PROBLEM:

The dummy in the figure shown below is driving his new VW$$Rabbit into a wall!$$ Will his shock$-$absorbing bumper $($k$2,$b$2)$ and his seat belts $($k$1,$ b$1)$ prevent him from hitting the windshield without breaking his collarbone?

DATA ON INJURIES $($SAE Handbook$)$

Seat belts must be tested to $3000$ lbs$.(1\mathrm{.}334$ x $104)$ N

Chest can sustain a force of $1500$ lbs$.$ distributed over $30$ in$2.$

Seat belt effective area $=30$ in$2$

Shoulder strap$-$seat belt combination $=60$ in$2$

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PHYSICAL PARAMETERS

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M$=1500$ Kg$,$ k$1=1$ x $104$ N$/$m$,$ b$1=500$ N$-$s$/$m

m$=100$ kg$,$ k$2=3$ x $105$ N$/$m$,$ b$2=8$ x $104$ N$-$s$/$m

Question: Create a Block Diagram and Bond Graph for simulation via MatLab.

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For reference, the simulation must produce a design of the seat belts and the bumper so that it satisfies the following conditions:

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$1.$ Passenger doesn't hit the windshield if he travels at $25$ and at $55$ mph$.$

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$2.-$ We must control the force acting on his chest and waist at $25$ mph and at $55$ mph$.$ Compare the data on injuries and determine if chest or internal injury occurs. If so that situation must be avoided.$(1)$ If he wears a seat belt only; $(2)$ If he wears a seat belt and a shoulder strap. What is the force acting on his chest and waist at $25$ mph and at $55$ mph$?$

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$3.$ What is the "critical", the maximum velocity $($when no injury occurs$)$ when impact occurs?$$ Hitting the windshield, chest injury, internal injury, seat belt failure, and strap failure, any of these should not occur.

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$4.$ What happens if he travels without a seat belt.$$ How long does it take for him to hit the windshield at $25$ mph$,40$ mph$,$ and $55$ mph$?$ What is the force acting on him on impact at $25$ mph$,40$ mph$,$ and $55$ mph$?$