Question

Determine the effective spring constant of the suspension system of a car. Consider a load of 4 passengers, each with a mass of 70 kg. The car suspension system consists of four identical springs, each with a spring constant k. When all four people get into the car, the tires are depressed by about Δx = 2.0 cm.

Answer 1

Answer:

The value of spring constant for each spring of the suspension system of a car   K = 343.35 $\frac{N}{cm}$

Explanation:

Total force on the springs = weight of the four passengers

⇒ F = 4 × 70 × 9.81

⇒ F = 2746.8 N

In the suspension system of the car the four springs are connected in parallel. So Equivalent spring constant is given by,

⇒ $K_{eq}$ = 4 K -------- ( 1 )

Depression in the spring Δx = 2 cm

Now the force  on the spring is given by

F = $K_{eq}$ × Δx

⇒ $K_{eq}$ = $\frac{2746.8}{2}$

⇒ $K_{eq}$ = 1373.4 $\frac{N}{cm}$

Now the spring constant for each spring = $\frac{K_{eq}}{4}$

⇒ K = $\frac{1373.4}{4}$

⇒ K = 343.35 $\frac{N}{cm}$

This is the value of spring constant for each spring of the suspension system of a car.