Car enthusiasts often lower their cars closer to the ground as a matter of style

Question

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.* In science, we try to represent complex systems with simplified representations. The new springs will be identical to the original springs except the force constant will be 4555.00 N/m smaller. When he 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 1455.00 kg, how much lower will the body drop compared to its original height? Number cm James was hoping for an overall lowering by 7 cm. Which of the following most closely describes James' results? The change is so small that James has largely wasted his time and money. The change is too drastic, causing the car to be un-driveable. James will be mostly pleased with the results. Note: 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

Explanation / Answer

initially mg = (4k)*x

1455*9.8 = 4k*(.12-.0855)

k = 103326.1

new k = 98871.1

mg = 4K'*x

x = .036 m or 3.6 cm

it is lowered to a height = 12-3.6 = 8.4 cm

Ans = 8.55-8.4 = .15 cm

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