Question

Four passengers with combined mass 250 kg compress the springs of a car by 4.00 cm when they enter it. Modeling the car and passengers as a single object on a single ideal spring, what is the resulting compression force?

A) 2500 N
B) 2450 N
C) 980 N
D) 1000 N

Answer 1

The resulting compression force is 2450 N.

Step-by-step explanation:

To find the resulting compression force, we can use Hooke's law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's law is F = kx, where F is the force, k is the force constant, and x is the displacement.

In this case, the compression of the spring is 4.00 cm, which is equal to 0.04 m. The combined mass of the passengers is 250 kg. Since the car and passengers are modeled as a single object, we can assume the mass is concentrated at the center of mass and use the equation F = kx to find the compression force.

Given that the compression is 0.04 m and the mass is 250 kg, we can calculate the resulting compression force as follows:

F = kx

F = (250 kg)(9.8 m/s^2)

F = 2450 N

Therefore, the resulting compression force is 2450 N, which corresponds to option B.