3 min readβ’june 8, 2020

Peter Apps

The linear motion of a system can be described by the displacement, velocity, and acceleration of its center of mass. The variables x, v, and a all refer to the center-of-mass quantities.

If you recall from kinematics there are a few major equations that relate **acceleration**, **displacement**, **initial and final velocity**, and **time** together.

βΆ In order to solve for a variable without having all four other quantities known, we look at the βVariable Missingβ column to pick the equation that best suits our question.

The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time.

Forces that the systems exert on each other are due to interactions between objects in the systems. If the interacting objects are parts of the same system, there will be no change in the center-of-mass velocity of that system.

Unfortunately, Newtonβs Second Law also includes pretty infamous problems such as **angular tension** and **apparent weight**. Not to worry though, weβre going to break them down:

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When youβre in an elevator going **downwards and speeding up** or going **upwards and slowing down** you tend to feel **lighter**. When youβre in an elevator going **upwards and speeding up** or going **downwards and slowing down** you tend to feel **heavier**. Why is that? To understand apparent weight fully, you must comprehend the four scenarios of the elevator problem:

The elevator accelerates upwards, but the inertia of a person would prefer to remain stationary, so the elevator floor must push up on the person with more force than their weight to accelerate them upwards. Therefore, Fn = ma + mg, so Normal Force is **greater than** true weight.

The elevator accelerates downwards, but the inertia of a person would prefer to remain stationary, so the elevator floor must drop out a little bit from underneath the person. This means the elevator floor must push up on the person less to support their weight, so Normal Force decreases. Therefore, Fn = mg - ma, so Normal Force is **less than** true weight.

If the acceleration of an elevator is zero, the elevator is either moving with constant velocity or at rest. When this is the case Fn = mg, so Normal Force is **equal to** the true weight.

If the elevator cable snaps, the elevator-person system will accelerate downwards at the rate of 9.8m/s/s (acceleration due to gravity). Since there is no contact between the floor of the elevator and the person Normal Force is zero. Therefore Normal Force is **less than** true weight.

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