I'm sorry this is kind of a long question. I've been staring at it for about an hour now and I have no clue where to even start. Thank you so much!!!!
A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 836 N.
1) As the elevator moves up the scale reading increases to 936 N, then decreases back to 836 N. Find the acceleration of the elevator.
2) As the elevator approaches the 74th floor, the scale reading drops to 782 N. What is the acceleration of the elevator now?
3) Using the results from parts a and b, explain which change in velocity, starting or stopping, would take the longer time.
4) What changes would you expect in the scale reading on the ride back down?
1)as the elevator accelerates upward, the student's weight increases
f = m a ... w = m a = m (g + e)
2)the elevator decellerates to a stop, so the student's weight is less than normal...same equations as #1
3)the greater the CHANGE in weight, the greater the acceleration ... which means a faster change in velocity (less time)
4)at the start (when the elevator accelerates downward) the scale will be below normal
once the downward velocity is constant, the scale will read normal
as the elevator is stopping at the bottom, the scale will be above normal
Thank you so much!! Would you mind explaining what the equations mean in #1? I know that Force= Mass x Acceleration, but what was the other equation?
Sorry my friend and I are both working on this together haha :)
It's strange, though, that both Kaylen and Maya said EXACTLY the same thing in posts made just one minute apart.
Please use the same name for your posts.
A classic example of Dissociative Identity Disorder . Look that up. I remember a great movie "Sybil" in 1976 on this. Sally Field was a great actress.
I wouldn't trust a person with Dissociative Identity Disorder.
To solve these problems, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
1) To find the acceleration of the elevator when the scale reading increases to 936 N and then decreases back to 836 N, we can use the equation:
Net force = mass × acceleration
The mass of the student stays constant, so we can ignore it for this problem. The net force is the difference between the maximum and minimum scale readings:
Net force = 936 N - 836 N = 100 N
Since the acceleration is the same throughout this process (assuming no other forces are acting on the student), we can use this equation to find it:
100 N = mass × acceleration
Therefore, the acceleration of the elevator is 100 N.
2) To find the acceleration of the elevator when the scale reading drops to 782 N as it approaches the 74th floor, we can use the same equation:
Net force = mass × acceleration
The net force is now the difference between the scale reading and the student's weight:
Net force = 782 N - 836 N = -54 N
The negative sign indicates that the net force is in the opposite direction of the student's weight. Again, assuming no other forces are acting on the student, we can use this equation to find the acceleration:
-54 N = mass × acceleration
Therefore, the acceleration of the elevator is -54 N.
3) From parts 1 and 2, we can see that the acceleration is positive when the elevator is moving up (part 1) and negative when the elevator is moving down (part 2).
When the elevator starts moving, the change in velocity (going from rest to a positive velocity) takes longer because it requires the elevator to overcome gravity and gain momentum. This means the elevator needs to accelerate over a longer period of time to reach a positive velocity.
When the elevator stops, the change in velocity (going from moving at a positive velocity to rest) takes less time because the elevator only needs to decelerate and overcome its initial momentum.
4) On the ride back down, assuming the elevator is at rest on the 74th floor, the scale reading would initially be the same as it was on the way up (836 N). As the elevator descends, the scale reading will decrease, indicating a decrease in the normal force acting on the student. This decrease is due to the negative acceleration of the elevator as it moves downward. The exact change in the scale reading will depend on the magnitude of the acceleration and other factors, such as air resistance, that may come into play.