Question

An object of mass m is placed in a lift moving upward with acceleration g/2. Find apparant weight.

Hint:

Lift accelerating UP $\implies$ feels heavier $\implies W_{app} = m(g+a)$
- Lift accelerating DOWN $\implies$ feels lighter $\implies W_{app} = m(g-a)$

Answer 1

Step 1: Understanding the Concept:
Apparent weight is the normal force exerted by a supporting surface (like the floor of a lift or a weighing scale) on an object. In an accelerating non-inertial frame of reference, we must account for pseudo forces. When a lift accelerates upwards, a pseudo force acts downwards on the object, increasing the normal force required to support it.

Step 2: Key Formula or Approach:
Let $N$ be the normal force (apparent weight).
From a non-inertial frame (inside the lift), the forces on the object are:
- Gravity downwards: $mg$
- Pseudo force downwards: $ma$
- Normal force upwards: $N$
For equilibrium inside the lift: $N = mg + ma = m(g + a)$

Step 3: Detailed Explanation:
The lift is moving upward with acceleration $a = g/2$.
Using the formula for apparent weight:
\[ W_{app} = N = m(g + a) \]
Substitute $a = g/2$:
\[ W_{app} = m\left(g + \frac{g}{2}\right) \]
\[ W_{app} = m\left(\frac{2g}{2} + \frac{g}{2}\right) \]
\[ W_{app} = m\left(\frac{3g}{2}\right) \]
\[ W_{app} = \frac{3}{2}mg \]
The apparent weight is greater than the true weight ($mg$).

Step 4: Final Answer:
The apparent weight is $\frac{3}{2}mg$.