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A 2kg block hangs without vibrating at t...

A `2kg` block hangs without vibrating at the bottom end of a spring with a force constant of `400 N//m`. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of `5 m//s^(2)` when the acceleration suddenly ceases at time `t = 0` and the car moves upward with constant speed `(g = 10 m//s^(2))`
What is the angular frequencyof the block after the acceleration ceases ?

A

`10sqrt(2) rad//s`

B

`20 rad//s`

C

`20sqrt(2) rad//s`

D

`32 rad//s`

Text Solution

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The correct Answer is:
A
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A block with a mass of 2 kg hangs without vibrating at the end of a spring of spring constant 500N//m , which is attached to the ceiling of an elevator. The elevator is moving upwards with an acceleration (g)/(3) . At time t = 0 , the acceleration suddenly ceases. (a) What is the angular frequency of oscillation of the block after the acceleration ceases ? (b) By what amount is the spring stretched during the time when the elevator is accelerating ? (c )What is the amplitude of oscillation and initial phase angle observed by a rider in the elevator in the equation, x = Asin (omega t + phi) ? Take the upward direction to be positive. Take g = 10.0 m//s^(2) .

Knowledge Check

  • Passage X) A 2kg block hangs without vibrating at the bottom end of a spring with a force constant of 400 N/m. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of 5m/ s^(2) when the accleration suddenly ceases at t=0 and the car moves upward with constant speed. (g=10m/ s^(2) ) What is the angular frequency of oscillation of the block after the acceleration ceases?

    A
    `10sqrt(2)`rad/s
    B
    `20 rad/s`
    C
    `20sqrt(2)`rad/s
    D
    `32 rad/s`

  • A 2kg block hangs without vibrating at the bottom end of a spring with a force constant of 400 N//m . The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of 5 m//s^(2) when the acceleration suddenly ceases at time t = 0 and the car moves upward with constant speed (g = 10 m//s^(2) The amplitude of the oscillation is

    A
    `7.5cm`
    B
    `5 cm`
    C
    `2.5 cm`
    D
    `1 cm`

  • Passage X) A 2kg block hangs without vibrating at the bottom end of a spring with a force constant of 400 N/m. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of 5m/ s^(2) when the accleration suddenly ceases at t=0 and the car moves upward with constant speed. (g=10m/ s^(2) ) The amplitude of the osciallations is

    A
    7.5 cm
    B
    5 cm
    C
    2.5 cm
    D
    1 cm

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