A 60.0 kg person stands on a scale in an elevator. (a) What does the scale read

Question

A 60.0 kg person stands on a scale in an elevator.

(a) What does the scale read (in N and in kg)when the elevator is at rest?
_____________ kg
_____________ N

(b) What does it read (in N and in kg) when the elevator is climbing at a constant speed of 3.5 m/s?
_____________ kg
_____________ N

(c) What does it read (in N and in kg) when the elevator is descending at 3.5 m/s?
_____________ kg
_____________ N

(d) What does it read (in N and in kg) when the elevator is accelerating upward at 3.5 m/s2?
_____________ kg
_____________ N

(e) What does it read (in N and in kg) when the elevator is accelerating downward at 3.5 m/s2?
_____________ kg
_____________ N

Explanation / Answer

As stated by newton's first law;
force = mass * acceleration (f=ma)
the force is measured in newtons, and 10 newtons roughly equal 1Kg (it's actually 9.81N per Kg if you need the accuracy - the same as the acceleration due to gravity)

when the elevator is stationary, or traveling at a constant speed, the acceleration is zero, and therefore there is no extra force on the scales, only that which is present due to the force of the weight of the person.
so the answer to a,b, and c is 60kg.

However, this changes when the elevator is under acceleration, as f=ma does no longer equal 0.

d) the force due to the acceleration is acting downwards, adding to the weight of the person, so they weigh;
60kg + (60*3.5/10) = 81Kg (10N of force = 1Kg)
(thinking about it, when a lift accelerates upwards, you feel like your knees will buckle and you feel heavier)

e) the force due to the acceleration is acting upwards, away from the scales, and so the person weighs less this time
60Kg - (60*3.5/10) = 39Kg
(again, thinking about it, when a lift drops downwards, you feel lighter)

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