What is the Force Constant k of a Spring?

AI Thread Summary
To find the force constant k of a spring used to stop a subway train, the initial kinetic energy of the train must be equated to the potential energy stored in the spring. The train's mass is 4.50 × 10^5 kg, and it is brought to a stop from a speed of 0.500 m/s over a distance of 0.900 m. The equation k = mg/x can be applied, but the correct method involves calculating the initial kinetic energy (KE) and setting it equal to the spring's potential energy (PE). The initial KE is determined using the formula KE = 0.5mv^2, and the final potential energy of the spring is PE = 0.5kx^2. Understanding the conservation of energy principle is crucial for solving this problem correctly.
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Homework Statement



A 4.50 ✕ 10^5 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.900 m by a large spring bumper at the end of its track. What is the force constant k of the spring?

M- 4.50E5 kg
IV- .5m/s
FV- 0m/s

Homework Equations


k=mg/x
F=-kx
PE = (.5)kx^2

The Attempt at a Solution


k=(450000kg)(9.81m/s^2)/ .9 = 4900000, which isn't the right answer. Can someone help me out?
 
Last edited:
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Have you read anything about the concept of potential energy of a spring?This question is directly based on that..
The kinetic energy of the train is being converted in the potential energy of spring?
 
Well I know PE = (.5)kx^2, but I am afraid I don't know how to plug in the numbers.
 
What's the intial kinetic energy (KE) of the train?
KE will = 0 when v = 0 (why is this true?)
Due to conservation of potential energy, initial(KE+PE) = final(KE+ E)
 

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