The Lift And The Particle.........

Classical Mechanics Level 3

A particle is dropped from the top of a lift of height 'x' m, just the instance when the lift starts moving from rest . If the lift moves with an acceleration of 4m/s^2 .Then find the height of the lift ,if the particle travels a distance of 5 m before hitting the base of the lift.

Note: Take g=10 m/s^2 , neglect air resistance.

6 4 5 3

1 solution

Kartikay Shandil
Jun 23, 2014

The solution of this problem comes from the fact that the base travels a distance 'x' m less than the particle. Now to solve using the second equation of motion S=ut+1/2at^2. S=5 (given). For lift S='x'+1/2 a1 t^2. a1=4m/s^2. ----(1) For particle S='1/2 a2 t^2. a2=10m/s^2 ----(2).(acc. due to gravity). Now solving (2) we get t=1sec. put t=1 in (1) we get 'x' =3 .i.e the answer required

My solution is that First we come in the frame of lift, In this frame the particle is accelerating downward with (10+4)m/s^{2} and distance covered is 'x' i.e the height of lift Using equation x=1/2 * 14 * t^{2} t^{2} = x/7 ------(1) Second we come in the frame of ground, In this frame the particle is accelerating downward with 10m/s^{2} and distance travelled is 5m(Given) Using equation 5=1/2 * 10 * t^{2} t^{2} = 1------(2) Comparing (1) and (2) x=7m

Ritesh Yadav - 6 years, 11 months ago

how a particle can travel distance more than the height of lift even when the lift is accelerating upward ?

Ritesh Yadav - 6 years, 11 months ago

Sorry There was a bit of a confusion ,the lift is moving downwards. This can be easily seen as the downward direction is taken as +ve as g is given =+10 instead of -10

Kartikay Shandil - 6 years, 11 months ago

Hey it should be mentioned that the lift is moving downward

jwalandhar girnar - 6 years, 11 months ago

This can be easily seen as the downward direction is taken as +ve as g is given =+10 instead of -10

Kartikay Shandil - 6 years, 11 months ago

The Lift And The Particle.........

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