An 18000 kg freight car rests against a spring bumper at the end of a railroad track. The spring has constant k=3.2×10^5 N/m. The car is hit by a second car of 9400 kg mass moving at 8.0 m/s , and the two couple together.
Find the maximum compression of the spring.
Find the speed of the two cars when they rebound together from the spring.
here,
mass of freight car , m1 = 18000 kg
mass of second car , m2 = 9400 kg
initial speed of second car , u2 = 8 m/s
let the final speed after the collison be v
using conservation of momentum
m2 * u2 = (m1 + m2) * v
9400 * 8 = ( 9400 + 18000) * v
solving for v
v = 2.74 m/s
spring constant , K = 3.2 * 10^5 N/m
let the maximum compression of the spring be x
using conservation of energy
0.5 * K * x^2 = 0.5 * ( m1 + m2) * v^2
3.2 * 10^5 * x^2 = (18000 + 9400) * 2.74^2
solving for x
x = 0.8 m
the maximum compression of the spring is 0.8 m
the speed of the two cars when they rebound together from the spring is 2.74 m/s
An 18000 kg freight car rests against a spring bumper at the end of a railroad...
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