Question

In a railroad switchyard, a rail car of mass 41,700 kg starts from rest and rolls down a 2.65-m-high incline and onto a level stretch of track. It then hits a spring bumper, whose spring compresses 79.4 cm. Find the spring constant.

Answer 1

The spring constant is 3.44x10⁶ kg/s².

Step-by-step explanation:

We cand find the spring constant by conservation of energy:

`E_(i) = E_(f)`

`mgh = (1)/(2)kx^(2)` (1)

Where:

m is the mass = 41700 kg

g is the gravity = 9.81 m/s²

h is the height = 2.65 m

x is the distance of spring compression = 79.4 cm

k is the spring constant =?

Solving equation (1) for k:

`k = (2mgh)/(x^(2)) = (2*41700 kg*9.81 m/s^(2)*2.65 m)/((0.794 m)^(2)) = 3.44 \cdot 10^(6) kg/s^(2)`

Therefore, the spring constant is 3.44x10⁶ kg/s².

I hope it helps you!