A man stands on the floor of a lift that accelerates upwards; how does the normal reaction on his feet compare with his weight?

Introduction / Context:
Situations involving people standing in accelerating lifts are standard examples used in Newtonian mechanics to illustrate how apparent weight changes with acceleration. The normal reaction force from the lift floor is what a weighing machine would read, and it represents how heavy the person feels. This question asks what happens to that reaction force when the lift accelerates upwards.

Given Data / Assumptions:

• A man of mass m stands on the floor of a lift.
• The lift accelerates upwards with uniform acceleration a.
• The acceleration due to gravity is g, directed downward.
• We neglect the mass of the lift and any friction in the cables.

Concept / Approach:
The key idea is to apply Newton second law to the man in the non accelerating frame of the ground. The forces on the man are his weight mg acting downward and the normal reaction N from the floor acting upward. When the lift accelerates upward with acceleration a, the man also accelerates upward with acceleration a. Newton second law then gives N - mg = m * a. Solving for N shows that N = m(g + a), which is clearly greater than mg as long as a is positive. Thus, the reaction force is greater than the man true weight and he feels heavier.

Step-by-Step Solution:
Step 1: Draw a free body diagram for the man: weight mg downward, normal reaction N upward. Step 2: The lift and the man accelerate upward with acceleration a, so the man acceleration is upward. Step 3: Apply Newton second law in the vertical direction: net force upward = m * a. Step 4: The net upward force is N - mg, so N - mg = m * a. Step 5: Rearrange to obtain N = mg + m * a = m(g + a). Step 6: Since a is positive for upward acceleration, g + a is greater than g, so N is greater than mg.

Verification / Alternative check:
If the acceleration a is zero, the lift moves at constant speed or is at rest, and N becomes mg, which matches the usual weight. If the lift accelerates upwards with a small a, the reaction becomes slightly larger than mg, matching the feeling of being pressed harder against the floor. In the extreme case where the acceleration is equal to g upwards, N would be 2mg, so the man would feel twice as heavy. These limits are consistent with the formula N = m(g + a) and confirm that N is greater than mg when a is positive.

Why Other Options Are Wrong:
Less than the weight of the man: This would occur if the lift accelerates downward, not upward.

Equal to the weight of the man: This only holds when the lift has zero acceleration, that is, when it is at rest or moving with constant velocity.

Zero, as if the man were weightless: This would correspond to free fall, where the lift accelerates downward with acceleration equal to g, not to an upward accelerating lift.

Common Pitfalls:
Learners sometimes confuse apparent weight with true weight and forget to consider the direction of acceleration. Another frequent mistake is to write N = mg - m * a regardless of direction, without carefully setting up the sign convention. The safe method is always to draw a free body diagram, define upward as positive and then apply Newton second law systematically. Doing this consistently makes it clear that upward acceleration increases the normal reaction above mg.

Final Answer:
When the lift accelerates upwards, the reaction force on the floor is greater than the weight of the man.