The car has an inertia of 500 kg and is 4.5 m long. It should be able to accelerate from rest to 29 m/s at least 50 times before the spring needs winding. The spring runs the length of the car, and a full winding compresses it to half this length. In order to meet the acceleration requirement, what must the value of the spring constant be?
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Kinetic energy imparted to the car (by spring) = 1/2 m v² (as u =0)
KE imparted during 50 times = 50 * 1/2 m 29² J
compression of the spring = x = 4.5 / 2 m = 2.25 m
Potential energy given out by the spring = 1/2 k x² = 1/2 k 2.25² J
Law of Energy conservation: 50*1/2 * 500* 29² = 1/2 k * 2.25²
k = spring constant = 4153 kN/m
KE imparted during 50 times = 50 * 1/2 m 29² J
compression of the spring = x = 4.5 / 2 m = 2.25 m
Potential energy given out by the spring = 1/2 k x² = 1/2 k 2.25² J
Law of Energy conservation: 50*1/2 * 500* 29² = 1/2 k * 2.25²
k = spring constant = 4153 kN/m
kvnmurty:
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