o: A spring can only be compressed so far before its coils touch. At that point

Question

o: A spring can only be compressed so far before its coils touch. At that point any force is transmitted through it as if it were a solid piece of metal. (i.e, once it compresses to its limit it cannot hold any additional spring potential energy. Aside: Batman never revealed the location of his secret "Bat-Cave" anyone before he and Robin were abducted by aliens and taken to the planet Mongo by Ming the merciless. The setup: You are driving your car (mass-1234. kg, including you) 29 miles/hr on a level but very twisty dirt road in the mountains when you swerve sideways to avoid hitting a Sasquatch. You maintain your speed, and think you are going to crash into a sheer cliff and die, but instead (to your surprise) you swish through some old vines and decaying camouflage into a hidden tunnel entrance. Before you can hit the breaks your car rolls down a steep hill into the murky darkness (the "bat"-lights all burned out 30.27 years ago but that doesn't matter because the "bat"-nuclear-generator went off line in the Oct 7 1983 earthquake) until it (your car with you in it) reaches the bottom 123 feet below, at which point it encounters an emergency "runaway car" buffer stop The buffer stop consists of two identical springs in housings, mounted as shown, which are initially uncompressed. The buffer stop also has a mechanism with an internal latch that keeps the spring from re expanding after it gets compressed. Latch Latch doesn't affect Spring while it is compressing Start of Once compressed latch snicks closed and spring cannot expand Fully Compression 2 compresses both buffer-stops the same distance. The spring constant of EACH individual buffer Your car stop is K-500,000N/m. The max compression of each stop is 1.000m and (obviously) there are a total of two buffer springs. Behind the buffer stop (also not shown in the eerie pitch darkness) is a sheer wall of ite with small (4.5 foot tall) tunnels leading off to the left and right (one in each direction

Explanation / Answer

given mass of car = 1234 kg

speed of car v = 29 mph = 12.9642 m/s

depth of cave, d = 123 feet = 37.49 m

number of springs = 2

spring constantr of each spring, k = 500,000 N/m

maximum compression = 1m

6. maximum compression energy that can be absorbed by pair of springs = 2*0.5*k*1^2 = 500,000 J

7. total energy of car when it reaches the springs = 0.5mv^2 + mgh = 0.5*1234*12.9642^2 + 1234*9.81*37.49

Et = 557536.18 J

this is more than 500,000 J by 57536.181 J

hence

total energy absorbed by the springs when the cart crashed = 500,000 J

8. after the spring is fully compressed, let the spe3ed of the car be u

then 0.5*1234*u^2 = 757536.181

u = 9.6566 m/s = 21.58 miles per hour

9. firs of all, some extra energy has to be lost due to friction of tyres and the path that included wines and other things

so the final speed has to be lower than 21 miles per hour

so thedre is a great chance of surviving this accident for the driver

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