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23 September, 10:11

A lamp hangs vertically from a cord in a descending elevator that decelerates at 1.7 m/s2. (a) if the tension in the cord is 63 n, what is the lamp's mass? (b) what is the cord's tension when the elevator ascends with an upward acceleration of 1.7 m/s2?

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  1. 23 September, 10:32
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    (a)

    The formula is:

    ∑ F = Weight + T = mass * acceleration

    as the elevator and lamp are moving downward, I choose downward forces to be positive.

    Weight is pulling down = + (9.8 * mass)

    Tension is pulling up, so T = - 63

    Acceleration is upward = - 1.7 m/s^2

    (9.8 * mass) + - 63 = mass * - 1.7

    Add + 63 to both sides

    Add (mass * 1.7) to both sides

    (9.8 * mass) + (mass * 1.7) = 63

    11.5 * mass = 63

    mass = 63 / 11.5

    Mass = 5.48 kg

    (b)

    Since the elevator and lamp are going upward, I choose upward forces to be positive.

    Weight is pulling down = - (9.8 * 5.48) = - 53.70

    Acceleration is upward, so acceleration = + 1.7

    -53.70 + T = 5.48 * 1.7

    T = 53.70 + 9.316 = approx 63 N

    The Tension is still the same - 63 N since the same mass, 5.48 kg, is being accelerated upward at the same rate of 1.7 m/s^2
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