VECTORS AND FORCES

III. Elevators and Gravity
Before you start, it would be most helpful if you understood what weight and gravity is about (see: Weight, Mass and Gravity).

When you're standing still, there is actually a force pushing you up (remember Newton's Third Law of Motion?) It doesn't matter if you're standing on the grass or in a motionless lift, you will experience 2 forces: Gravity and a reactive force. The reactive force only exists if there is another force present.

The 2 forces can be combined to find the resultant force (daya paduan).

F2 + (- F1) = F
(Remember, they are in opposite directions so one has to be negative!)

To distinguish between the different forces in the following examples, let's write F2 as R. F1 is Weight, so let's write is as mg

R - mg = F


When the elevator is still, the person inside is not accelerating (a = 0). Therefore:

R - mg  = ma
R - mg  = m(0) 
R - mg  = 0 
R  = 0 + mg
R  = mg

So when standing still, R = mg
That makes sense, doesn't it? If you're being forced downwards by gravity, you need an upwards force that has the same magnitude (strength) to prevent your from moving. If one of the forces is greater than the other, you will start moving in that direction.


When the elevator is accelerating downwards, the acceleration has a negative value (up is positive)

R - mg  = m(-a) 
R - mg  = -ma 
R  = -ma + mg
R  = mg - ma

So when accelerating downwards, R = mg - ma<
In the 1st equation, R is the same as mg. But now, R is LESS than mg. (The equation says "mg MINUS something," which means the value of R is reduced) This makes sense: The upwards force is not strong enough to cancel out the downwards force, which is why the lift accelerates downwards.


When the elevator is accelerating upwards, the acceleration has a positive value.

R - mg  = ma 
R  = ma + mg

So when accelerating upwards, R = mg + ma
Now, R is GREATER than mg. (The equation says "mg PLUS something," which means the value of R is increased) This makes sense: Some of the upwards force has to be greater than the downwards force in order to lift an objectThe upwards force is not strong enough to cancel out the downwards force, which is why the lift accelerates downwards.


Ok, we've dealt with acceleration. What about moving up/down with constant velocity (halaju seragam)? Well, remember that there is no acceleration here, so R = mg as if the lift was not moving

Important note: No extra force is needed to keep an object moving at a constant velocity. Inertia causes it to continue moving, even when there is no more force involved.

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