Car enthusiasts often lower their cars closer to the ground as a matter of style. James wants to lower his car by replacing all four of his original coil springs with new ones offered as an option by the car manufacturer. Note that changing the coil springs on a car can unsafely affect its handling. Consult your national or state laws before altering the suspension on any car. The new springs will be identical to the original springs, except the force constant will be 5855.00 N/m smaller. When James removes the original springs, he discovers that the length of each spring expands from 8.55 cm (its length when installed) to 12.00 cm (its length with no load placed on it). If the mass of the car body is 1355.00 kg, by how much will the body be lowered with the new springs installed, compared to its original height?

Question

Physics

Arthur Olson

19 July, 16:34

Car enthusiasts often lower their cars closer to the ground as a matter of style. James wants to lower his car by replacing all four of his original coil springs with new ones offered as an option by the car manufacturer. Note that changing the coil springs on a car can unsafely affect its handling. Consult your national or state laws before altering the suspension on any car. The new springs will be identical to the original springs, except the force constant will be 5855.00 N/m smaller. When James removes the original springs, he discovers that the length of each spring expands from 8.55 cm (its length when installed) to 12.00 cm (its length with no load placed on it). If the mass of the car body is 1355.00 kg, by how much will the body be lowered with the new springs installed, compared to its original height?

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Answers (1)

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Johan · Answer 1

0.05 cm

Explanation:

The compression of the original spring = 12 - 8.55 cm = 3.45 cm = 0.0345 m

By Hooke's law, F = ke

Where F is the applied force, k is the spring constant and e is the extension or compression. In the question, F is the weight of the car.

k = F/e = 1355 * 9.8 / 0.0345 = 384898.55 N/m

This is the spring constant of the original spring. The question mentions that the force constant of the new spring is 5855.00 N/m smaller. Hence, the force constant of the new spring is 384898.55 - 5855 = 379043.55 N/m

With the new spring installed, the compression will be

e = F/k = 1355 * 9.8 / 379043.55 = 0.035 m = 3.5 cm

The difference in the compressions of both springs = 3.5 cm - 3.45 cm = 0.05 cm