(7%) Problem 5: A 42 × 10° kg subway train is brought to a stop from a speed of

Question

(7%) Problem 5: A 42 × 10° kg subway train is brought to a stop from a speed of 0.75 ms in 0.39 m by a large spring bumper at the end of its track. What is the force constant k of the spring in N m? Grade Summary Deductions Potential 1113568 4% 96% cos0 789 HOME sin0 cotan0asin acos0 atan0 acotan sinhO cosh0 tanh cotanh0 Submissions ts remaining: 6 (400 per attempt) detailed view END 4% Degrees Radians NBACKSPACEEL CLEAR Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback.

Explanation / Answer

given, mass of train, m = 4.2*10^5 kg
initial speed, u = 0.75 m/s
final speed, v = 0 m/s
distance d= 0.39 m

so loss of KE = 0.5mu^2 - 0.5mv^2
gain in spring PE = 0.5kd^2 ( where k is spring constnat of the spring)
hence
from conservation of energy
0.5mu^2 = 0.5kd^2
4.2*10^5*0.75^2 = K*0.39^2
k = 1553254.4378 N/m

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