Question

Question-2 An elevator whose floor to ceiling height is 2.75m starts ascending with constant upward
acceleration of 1.2m/s^2. Two seconds after the start, a loose bolt drops from the ceiling towards the floor
of the elevator. Calculate:
11
Time taken by the bolt to reach the elevator floor.
Displacement of the bolt during that time
The distance travelled by the bolt during the same time.​

Answer 1

(1) Time taken by the bolt to reach the elevator floor = 0.7 seconds

(2) Displacement of the bolt during that time = 0.721 m

(3) The distance travelled by the bolt during the same time = 1.31 m

Explanation:

Given:

Height of the ceiling h = 2.75 m

Acceleration of the lift upwards = +1.2 m/s²

In the frame of reference of elevator, the acceleration of the bolt will be (a+g) = 9.8 + 1.2 = 11 m/s²

In this frame of reference the bolt starts from rest and covers a distance of 2.75 m

(1) Using the second equation of motion

$h=ut+\frac{1}{2}at^2$

$2.75=0\times t+\frac{1}{2}\times 11\times t^2$

$\implies 5.5=11t^2$

$\implies t^2=\frac{5.5}{11}=0.5$

$\implies t=\sqrt{0.5}=0.7$ seconds

Thus, the time taken by the bolt to reach the elevator floor = 0.7 seconds

(2) If seen in the frame of reference of earth, the bolt will first go upwards and then downwards

The upward velocity of the elevator in 2 seconds

$v=u+at$

$v=0+1.2\times 2=2.4$ m/s

Therefore, displacement

Using the second equation of motion

$s=-2.4\times 0.7+\frac{1}{2}\times 9.8\times 0.7^2$

$\implies s=-1.68+2.401=0.721$ m

(3) The distance travelled by the bolt will be the upwards distance travelled by the bolt + the distance taken from here to fall on the floor of the elevator

Therefore,

upward distance

Using the third equation of motion

$v^2=u^2-2as'$

$\implies 0^2=2.4^2-2\times 9.8s'$

$\implies s'=\frac{2.4^2}{2\times 9.8}=0.294$ seconds

While falling too the bolt will cover this distance + the displacement

Therefore, the total distance travelled by the bolt

$=2\times 0.294+0.721$

$=1.31$ m

Hope this answer is helpful.

Know More:

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