Ask Question
14 February, 14:13

A runaway railroad car with mass 3.0 ✕ 105 kg coasts across a level track at 2.0 m/s when it collides elastically with a spring-loaded bumper at the end of the track. If the spring constant of the bumper is 2.0 ✕ 106 N/m, what is the maximum compression of the spring during the collision?

+5
Answers (1)
  1. 14 February, 15:00
    0
    Maximum compression = 77.5cm

    Explanation:

    We are given that;

    mass; m = 3 x 10^ (5) m/s

    Speed; v = 2 m/s

    Spring Constant; k = 2 x10^ (6) N/m

    From conservation of energy. Kinetic energy is transformed into potential energy of spring

    Kinetic energy = (½) mv ²

    Elastic potential energy of spring = (½) kΔx²

    Thus,

    (½) mv² = (½) kΔx²

    1/2 will cancel out and we have;

    mv² = kΔx²

    Now we are looking for maximum compression which is Δx, so let's make Δx the subject of the formula;

    Δx² = mv²/k

    Δx = √ (mv²/k)

    Plugging in relevant values;

    Δx = √ ((3 x 10^ (5) x 2²) / 2 x10^ (6))

    Δx = √ (0.6) = 0.775 m ≈ 77.5 cm
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A runaway railroad car with mass 3.0 ✕ 105 kg coasts across a level track at 2.0 m/s when it collides elastically with a spring-loaded ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers