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Example 6.8 To simulate car accidents, automanufacturers study the collisions of movingcars with mounted springs of different springconstants. Consider a typical simulation witha car of mass 1000 kg moving with a speed18.0 km/h on a smooth road and collidingwith a horizontally mounted spring of springconstant 6.25 × 103 N m-1, what is themaximum compression of the spring?

Answer»

let max compression is x m ...

m = 1000 kg ....

v = 18 km / hrs = 5 m / s ....

k = 6250 N / m ....

when the car collides wid the spring ..

the energy in car is KE = 1 / 2 * m * v^2...

energy of spring = 1 / 2 * k * x^2..

Now ... 1 / 2 * m * v^2= 1 / 2 * k * x^2

----> 1000 * 25 = 6250 * k^2

----> k^2= 4

----> k = 2 m ... (ans) ...



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