Home
Class 11
PHYSICS
A block with a mass of 2 kg hangs withou...

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)`.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
(a) Angular frequency
` omega = sqrt((k)/(m))` or `omega = sqrt((500)/(2))`
or `omega = 15.81 rad//s`
(b) Equation of motion of the block (while elevator is accelerating) is,

` kx - mg = ma = m(g)/(3)`
`:. x = (4mg)/(3k)`
`= ((4)(2)(10))/((3)(500)) = 0.053 m`
or `x = 5.3 cm`
(c) (i) In equilibrium when the elevator has zero acceleration, the equation of motion is,

`kx_(0) = mg`
or `x_(0) = (mg)/(k) = ((2)(10))/(500)`
`= 0.04m = 4cm`
`:.` Amplitude `A = x - x_(0) = 5.3 - 4.0`
` = 1.3cm`
(ii) At time `t = 0`, block is at `x = - A`. Therefore, substituting `x = - A` and `t = 0` in equation,
` x = Asin (omega t + phi)`
We get initial phase `phi = (3pi)/(2)`
.
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    DC PANDEY|Exercise Level 1 Assertion And Reason|10 Videos

  • SIMPLE HARMONIC MOTION

    DC PANDEY|Exercise Level 1 Single Correct|24 Videos

  • SIMPLE HARMONIC MOTION

    DC PANDEY|Exercise Example Type 13|3 Videos

  • SEMICONDUCTORS AND ELECTRONIC DEVICES

    DC PANDEY|Exercise More than One Option is Correct|3 Videos

  • SOLVD PAPERS 2017 NEET, AIIMS & JIPMER

    DC PANDEY|Exercise Solved paper 2018(JIPMER)|38 Videos

Similar Questions

Explore conceptually related problems

A block of mass 1kg hangs without vibrating at the end of a spring whose force constant is 200(N)/(m) and which is attached to the ceiling of an elevator. The elevator is rising with an upward acceleration of (g)/(3) when the acceleration suddenly ceases. The angular frequency of the block after the acceleration ceases is

A block of mass 1kg hangs without vibrations at the end of a spring with a force constant 1 N//m attached to the ceilling of an elevator. The elevator is rising with an upward acceleration of g//4 . The acceleration of the elevator suddenly ceases. What is the amplitude of the resulting oscillations?

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 spring of spring constant 200 N//m has a block of mass 1 kg hanging at its one end and form the other and the spring is attached to a celling of an elevator. The elevator rises upwards with an acceleration of g//3 . When acceleration is suddenly ceased , then what should be the angular frequency and elongationduring the time when the elevator is accelerating?

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 spring of spring constant 200N//m has a block of mass 1kg hanging at its one end and other end of spring is attached to ceiling of an elevator. The elevator is rising upwards with an acceleration g//3 . What should be the angular frequency and elongation during the time when the elevator is accelerating?

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

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

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 initial phase angle observed by a rider in the elevator, taking upward directioin to be positive and positive extreme position to have pi/2 phase constant, is equal to

A pulley with two blocks system is attached to the ceiling of a lift upward with an acceleration a_(0) . Find the deformation in the spring.