Physics

Problem

A mass

m

is suspended from a light spring of force constant

k

which is attached to the ceiling of an elevator. The elevator accelerates uniformly upward with acceleration

a

. a. (i) Draw a clearly labelled free–body diagram of the mass and hence derive an expression for the extension

e

produced in the spring in terms of

m

g

a

and

k

. b. (ii) Taking

m = 2\,\text{kg}

k = 500\,\text{N}\,\text{m}^{-1}

and

a = 2\,\text{m}\,\text{s}^{-2}

, calculate the numerical value of

e

. c. (iii) If the elevator now moves downward with a constant acceleration of

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

, comment on whether the spring remains stretched, becomes slack, or is in a state of compression. Justify your answer with calculation.