You stand on a bathroom scale that rests on the floor of an elevator. (Don\'t as

Question

You stand on a bathroom scale that rests on the floor of an elevator. (Don't ask why!) Standing on the scale compresses internal springs and activates a dial that indicates your weight in newtons. When the elevator is at rest, the scale reads 600 N. Then the elevator begins to move upward with a constant acceleration of 2.00 m/s/s.

Determine your true mass.
Determine the scale reading while the elevator is accelerating.
If you read the scale without realizing that it is accelerating upward what might you think your mass is?
What would your answers be if the elevator is accelerating downward?

Explanation / Answer

I'm not sure how old this is, but here's my answer anyway:

Determine mass:

Easy! We know that: F = ma

We also know weight in this case, is the force. So, W = ma

We also know that gravity is our acceleration at rest! So, W = mg

So to manipulate the equation to find mass, m = W/g

So... m = 600N / 9.8m/s2

m = 61.2kg

Determine weight while accelerating up:

But this requires a little thinking... we know F = ma, but what's going on that's different this time?

Acceleration is added to the mix... and we know from our every day experiences that when we are accelerated up or forward, we feel the force pushing us down or back. Think about being in a car or... elevator.

We have 2m/s2 , which is thankfully given to us, and the gravity from before!

So is the 2m/s2 pushing us up, or down? Well, if the elevator is moving up we know that our body will want to remain at its natural state of rest, below us as we move up. So we're being pushed down by the 2m/s2 AND the 9.8m/s2 of gravity! So our acceleration will be both combined!

F = ma

W = ma

W = 61.2kg (2m/s2 + 9.8m/s2 )

W = 722.2N

Determine weight while accelerating down:

Hey, this should be easy if you read the part about accelerating up! Just look at my math and it will make sense!

F = ma

W = ma

W = 61.2kg ( - 2m/s2 + 9.8m/s2 )

W = 477.4N

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