Solving Dynamics Homework: Man on Elevator, 60 kg Mass

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To solve the dynamics problem of a man standing on a scale in an accelerating elevator, the correct approach involves calculating the net force acting on the man due to both gravitational and elevator acceleration. The gravitational force (F2) is 588.6 N downward, while the force due to the elevator's upward acceleration (F1) is 300 N upward. The teacher's method of finding the reading on the scale by subtracting the upward force from the downward force is accurate, resulting in a total force of 888.6 N downward. The student's alternative method of calculating the net acceleration and then determining the force is incorrect because it overlooks the direct impact of the elevator's acceleration on the scale reading. Understanding the interaction of these forces is crucial for accurately determining the scale's reading.
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Homework Statement



I'm confused w/ a dynamic question our teacher showed us today. we just started dynamics and I'm in grade 11. I made a horrible diagram on ms paint but I believe it will suffice :) A man is standing in an elevator on a scale. The elevator is moving up at 5m/s^2 and then there is the obvious gravitational pull. What will be the reading on the scale, in Newtons (so force?), if the man's mass is 60 kg?

Elevator_PhysicsQ.jpg


Homework Equations



She told us to use a= FR/m

The Attempt at a Solution



The thing is she solved it for us and I can't seem to understand her steps. She says to find the individual Forces of both accelerations. So F=ma

F1= 60kg * 5 m/s^2 [UP]
F2= 60kg * 9.81 m/s^2 [DOWN]

This is the part that confuses me: FR= F2-F1
We've never done subtraction of vectors before, and she explained that we change the direction of the second vector and just add it.

Therefore, F1= 300N [UP] , F2= 588.6N [DOWN]
which becomes: 588.6N [DOWN] + 300N [DOWN] = 888.6N [DOWN] <--- HER FINAL ANSWER

My first question is since the whole system is affected by the two accelerations doesn't "cancel" out? In other words, although he is moving up at 5m/s^2 and down at 9.81m/s^2, the scale is also experiencing those movements, therefore it will almost be like "at rest". If I was to do it, I would ignore them, and simply calculate his weight: 60kg * 9.81 m/s^2 [DOWN] = 588.6N [DOWN]. If not, I would add the two accelerations and get: 9.81m/s^2 [DOWN] + 5m/s^2 [UP] = 4.81m/s^2 [DOWN] (basically subtracting them and keeping the larger ones direction). After, I'd multiply that by mass and get: 60kg * 4.81m/s^2 [DOWN] = 288.6N [DOWN].

Are one of my methods and/or my teacher's right? If not, please explain why. Thanks!

Homework Statement


Homework Equations


The Attempt at a Solution

 
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