Auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a car of mass 1500 kg moving with a speed of 36 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant 7.5 x 10³ N m-¹.
Find the maximum compression of the spring.
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Explanation:
Solution:
At maximum compression, KE of car gets converted completely into PE of the spring.
KE of car = K = 1/2 mv²
= 1/2×1500x10x10 (v=36x5/18= 10 m/s)
= 7.5 × 10¹ J
At maximum compression x PE, V of the spring = KE, K of car
V = 1/2kx²m = 7.5×10^4 J
Xm=√2x7.5×10^4/7.5×10^3
= 4.47m
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