A man of mass m is standing on a lift which moves down with an upward acceleration a. Find the pseudo force acting on the man as observed by himself. Find the pseudo force acting on the man if the lift falls freely.

Explanation

To solve the problem, we will analyze the two scenarios separately: when the lift moves down with an upward acceleration \( a \) and when the lift falls freely.

### Step 1: Pseudo Force when the Lift Moves Down with Upward Acceleration \( a \)

1. **Understanding the Situation**: The man is in a lift that is moving downward but accelerating upward with an acceleration \( a \).
2. **Identifying the Pseudo Force**: In a non-inertial frame (the frame of the man in the lift), a pseudo force acts on the man. This pseudo force acts in the opposite direction to the acceleration of the lift.
3. **Direction of the Pseudo Force**: Since the lift is accelerating upward, the pseudo force will act downward.
4. **Calculating the Pseudo Force**: The magnitude of the pseudo force \( F_{\text{pseudo}} \) can be calculated using the formula:
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