When four people with a combined mass of 315 kg sit down in a 2000-kg car, they find that their weight compresses the springs an additional 0.90 cm. (a) What is the effective force constant of the springs?

3.43 x 10⁵ N/m

Explanation:

M = mass of the car alone = 2000 kg

m = mass of the four people combined = 315 kg

x = compression of the spring when there is car alone

x' = compression of the spring when there is car and four people = x + 0.009

k = spring constant

When there is car, the weight of the car is balanced by the spring force and the force equation is given as

k x = Mg

k x = (2000) (9.8)

k x = 19600 eq-1

When there is car and four people, the weight of the car and four people is balanced by the spring force and the force equation is given as

k x' = (M + m) g

k (x + 0.009) = (2000 + 315) (9.8)

k x + 0.009 k = (2000 + 315) (9.8)

using eq-1

19600 + 0.009 k = 22687

k = 3.43 x 10⁵ N/m