An elevator starts from rest at the bottom of a deep mine and carries a worker of…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

An elevator starts from rest at the bottom of a

2.0\,\text{km}

deep mine and carries a worker of mass

80\,\text{kg}

to the surface. The motion of the elevator is as follows: • it accelerates upward uniformly at

1.2\,\text{m\,s}^{-2}

for

5\,\text{s}

, • then moves at constant speed for the next

10\,\text{s}

, • and finally decelerates uniformly at

1.2\,\text{m\,s}^{-2}

so as to come to rest exactly at the surface. Take

g

at the surface as

9.80\,\text{m\,s}^{-2}

and Earth’s radius

R = 6.4\times10^{6}\,\text{m}

. (i) Derive an approximate expression for the acceleration due to gravity at a depth

d\,(\ll R)

below the Earth’s surface in terms of

g

d

and

R

. (ii) Using the expression from part (i), calculate the value of

g

at the bottom of the mine. (iii) Find the reading of the worker’s scale (a)

3.0\,\text{s}

after the elevator starts, (b) midway through the constant-speed section, and (c) just before the elevator stops at the surface. (iv) Identify the maximum and minimum values of the scale reading during the entire journey and state at which stage each occurs.

Related theory

Browse the problem library