Question

A man of mass $70$ $kg$ stands on a weighing scale in a lift which is moving.
(a) Upwards with a uniform speed of $10$ $m{s}^{-1}$.
(b) Downwards with a uniform acceleration of $5$ $m{s}^{-2}$.
(c) Upwards with a uniform acceleration of $5$ $m{s}^{-2}$.
What would be the reading on the scale in each case?
(d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

Answer 1

$\left(a\right)$. As the lift is moving at a uniform speed, acceleration $a=0$

$R=mg=70\times 10\Rightarrow 700N$

Reading on the weighing scale

$=700/g=700/10=70kg$

$\left(b\right)$ Mass of the man, $m=70kg$

Acceleration, $a=5m/s^2$ downward

Using Newtons second law of motion, we can write the equation of motion as:

$R+mg=maR=m(g-a)=70(10-5)=70\times 5=350N$

Reading on the weighing scale

$\Rightarrow 350g=350/10=35kg$

$\left(c\right)$ Mass of the man, $m=70kg$

Acceleration, $a=5m/s^2$ upward

Using Newtons second law of motion, we can write the equation of motion as:

$R-mg=maR=m(g+a)=70(10+5)=70\times 15=1050N$

Reading on the weighing scale

$\Rightarrow 1050/g=1050/10=105kg$

$\left(d\right)$ When the lift moves freely under gravity, acceleration $a=g$

Using Newtons second law of motion, we can write the equation of motion as:

$R+mg=maR=m(g-a)=m(g-g)=0$

Reading on the weighing scale $=0/g=0kg$

The man will be in a state of weightlessness.