A 1800 kg car moving at 20 m/s hits an initially uncompressed spring with a spring constant of 2.0 × 10⁶ N/m. The maximum compression of the spring is

Question

Quizplus · Accepted Answer

Before the collision, the car has a kinetic energy of:
KE = (1/2)mv^2 = (1/2)(1800 kg)(20 m/s)^2 = 360,000 J

When the car hits the spring, its kinetic energy is converted into potential energy stored in the compressed spring. At the maximum compression, all of the kinetic energy will be converted into potential energy.

The potential energy stored in a spring is given by:
PE = (1/2)kx^2
where k is the spring constant and x is the displacement (compression) of the spring.

Setting KE equal to PE, we get:
(1/2)mv^2 = (1/2)kx^2
Solving for x, we get:
x = sqrt((mv^2)/k) = sqrt((1800 kg)(20 m/s)^2/(2.0 × 10^16 N/m)) = 0.60 m

Therefore, the maximum compression of the spring is 0.60 m, which corresponds to choice B.

A 1800 Kg Car Moving at 20 M/s Hits an Initially