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26 March, 23:41

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?

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  1. 27 March, 00:06
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    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
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