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21 July, 14:02

An elastic towrope has spring constant 1300 N/m. It's connected between a truck and a 1900-kg car. As the truck tows the car, the rope stretches 55 cm. Starting from rest, how far do the truck and the car move in 1 min? Assume the car experiences negligible friction.

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  1. 21 July, 14:04
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    the truck and the car move 586.8 m

    Explanation:

    Hook's Law: Hook's law state that the force applied to an elastic material is directly proportional to its extension, provided the elastic limit is not exceeded.

    From hook's law,

    F = ke ... Equation 1

    Where F = applied force, k = force constant of the spring or elastic material, e = extension

    Given: k = 1300 N/m, e = 55 cm = (55/100) m = 0.55 m.

    Substituting these values into Equation 1,

    F = 1300 * 0.55

    F = 715 N.

    But Force (F) = ma ... Equation 2

    making a the subject of the equation,

    a = F/m ... Equation 3

    Where m = mass of the car, a = acceleration of the car.

    Given: m = 1900 kg, and F = 715 N

    Substituting these values into equation 3

    a = 715/1900

    a = 0.376 m/s²

    Using one of the equation of motion,

    S = ut + 1/2at² ... Equation 4

    Where S = distance covered, u = initial velocity of the car, t = time, a = acceleration

    Given: t = 1 min (1*60) = 60 s, u = 0 m/s (at rest), a = 0.376 m/s²

    Substituting these values into equation 4

    S = (0 * 60) + 1/2 (0.376*60²)

    S = (3600 * 0.376) / 2

    S = 586.8 m

    Therefore the truck and the car move 586.8 m
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