Question

A man of mass 70 $\text {kg}$ stands on a weighing scale in a lift which is moving

1. upwards with a uniform speed of 10 $\text m \,\text s^{-1}$ ,
2. downwards with a uniform acceleration of 5 $\text m \,\text s^{-2}$ ,
3. upwards with a uniform acceleration of 5 $\text m \,\text s^{-2}$ . What would be the readings on the scale in each case?
4. What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?

Answer 1

(a) Mass of the man, $\text m$ = 70 $\text {kg}$
Acceleration, $\text a$ = 0
Using Newton’s second law of motion, we can write the equation of motion as:
$\text R - \text {ma}$ = $\text {ma}$
Where, $\text {ma}$ is the net force acting on the man.
As the lift is moving at a uniform speed, acceleration $\text a$ = 0
$\therefore$ $\text R$ = $\text {mg}$
= 70 × 10 = 700 N
Reading on the weighing scale = $\frac{700}{\text g}$ = $\frac{700}{10}$ = 70 $\text {kg}$

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(b) Mass of the man, m = 70 $\text {kg}$
Acceleration, $\text a$ = 5 $\text m/\text s^2$ downward
Using Newton’s second law of motion, we can write the equation of motion as:
$\text R+\text{mg} = \text {ma}$
$\text R$ = $\text m$($\text g$ – $\text a$)
= 70 (10 – 5)
= 70 × 5 = 350 N
Reading on the weighing scale = $\frac{350}{\text g}$ = $\frac{350}{10}$ = 35 $\text {kg}$

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(c) Mass of the man, $\text m$ = 70 $\text {kg}$
Acceleration, $\text a$ = 5 $\text m/\text s^2$ upward
Using Newton’s second law of motion, we can write the equation of motion as:
$\text R$ – $\text {mg}$ = $\text {ma}$
$\text R$ = $\text m$($\text g+\text a$)
= 70 (10 + 5)
= 70 × 15
= 1050 N
Reading on the weighing scale = $\frac{1050}{\text g}$ = $\frac{1050}{10}$ = 105 $\text {kg}$

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(d) When the lift moves freely under gravity, acceleration $\text a$ = $\text g$
Using Newton’s second law of motion, we can write the equation of motion as:
$\text R+\text{mg} = \text {ma}$
$\text R$ = $\text m$($\text g$ – $\text a$)
= $\text m(\text g-\text g)$
= 0
Reading on the weighing scale =$\frac{0}{\text g}$= 0 $\text {kg}$
The man will be in a state of weightlessness.