# Apparent Weight

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Apparent weight

When body is at rest with no acceleration, R = W. Reading on the weighing machine reflects the true weight, W, force of gravity acting on our body (mg).

When we are in equilibrium, the normal reaction is equal to the weight.

Case of lift with upward acceleration

• As acceleration of lift is upward, the resultant force is upward.
• R = W + ma

Since R is greater than W, the weighing machine shows a reading greater than the actual force due to gravity (W), the person feels heavier or its apparent weight is heavier.

The person would also feel the same way when slowing down during a descent.

Case of lift with downward acceleration
– As acceleration of lift is downward, the resultant force is downward.
– R = W – ma

Since R is less than W, the weighing machine shows a reading which is a reading lesser than the actual force due to gravity – the person feels lighter or its apparent weight is lighter.

The person would also feel the same way when slowing down during an ascent.

Weightlessness

• If the acceleration a is equal to g, the lift is free-falling, then we have R = 0.
• The machine would register a zero reading and is not in contact with the body. Therefore, apparent weight is zero and the body experiences weightlessness.
• A body is said to be free-falling and experiencing apparent weightlessness if the only force acting on it is its true weight (mg) and its acceleration, a is equal to g.

For a force-time graph, area under graph is the impulse (Change in momentum)

Average force

$\left< F \right> = \frac{\Delta p}{\Delta t}$

For N number of collisions: $\left< F \right> = \Delta p \times \frac{N}{\Delta t}$

Area under average force graph = area under actual force graph.

$\left< F \right> = \Delta$ in momentum in one collision $\times$ collision frequency

$\left< F \right> = v \times \frac{dm}{dt}$