Question

A woman weighing $50kg$ stands on a weighing machine placed in a lift. What will be the reading of the machine, when the lift is? Take $g = 10m{s^{ - 2}}$
(A) Moving upward with a uniform velocity of $5m{s^{ - 1}}$
(B) Moving downward with an acceleration of $1m{s^{ - 2}}$

Answer 1

Hint we will use the concept of pseudo forces to approach the result. When the lift is moving upward a pseudo force is acting downward along with the weight of the woman and when the lift is moving downward then a pseudo force is acting upward opposite to the weight of the woman.

Complete Step by step solution
When lift is moving upward:
When lift is moving upward then the pseudo force acts on the downward direction along with the weight hence the reaction force i.e. reading on the weighing machine is,
Let the reaction force is $R$
Then,
Reaction force= weight + pseudo force
If $a$ be the acceleration by which lift is moving upward then pseudo force is given by $F = ma$
Hence the reaction force is,
$\Rightarrow$ $R = mg + ma \\\ R = m(g + a) \\\$
Here, lift is moving upward with constant velocity.
$\therefore a = 0$
Hence

$$R = mg + 0 \\\ R = mg \\\ R = 50 \times 10 \\\ R = 500N \\\$$

When lift is moving downward:
When lift is moving downward then the pseudo force acts on the upward direction opposite to the weight hence the reaction force i.e. reading on the weighing machine is,
Let the reaction force is $R$
Then,
Reaction force = weight – pseudo force
i.e. $R = mg - ma \\\ R = m(g - a) \\\$
given, $a = 1m{s^{ - 2}}$
hence, we get
$\Rightarrow$ $R = 50 \times (10 - 1) \\\ R = 50 \times 9 \\\ R = 450N \\\$

Hence the reading of the machine in both cases is $500N$ and $450N$ respectively.

Note We know that Newton’s law is valid only for inertial frames. If we want to use those laws into non inertial frames then we apply pseudo forces. These pseudo forces act as a correction term. If we work from an inertial frame, then there is no need for pseudo forces. The pseudo forces are also called inertial forces although their need arises because of the use of non-inertial frames.