What is the acceleration of the elevator in these scenarios?

In summary, the scale reading in an elevator changes as it moves up or down due to the normal force exerted on an object by the elevator floor. By using Newton's Second Law, the acceleration of the elevator can be determined by comparing the scale readings at different points. The acceleration can also be used to determine which change in velocity, starting or stopping, takes longer based on the forces involved.
  • #1
Ally385
16
0

Homework Statement


A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 828 N.
(a) As the elevator moves up, the scale reading increases to 919 N. Find the acceleration of the elevator.
(b) As the elevator approaches the 74th floor, the scale reading drops to 782 N. What is the acceleration of the elevator?
(c) Using your results from parts a and b, select which change in velocity, starting or stopping, takes the longer time. Explain.

Homework Equations



f=ma

The Attempt at a Solution



I've done all of these problems twice and I can't figure out the solution. I thought you would just find the average acceleration but I guess not.
 
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  • #2


Start by identifying the forces acting on the student, then apply Newton's 2nd law: ƩF = ma.
 
  • #3


I know that the scale is exerting a force but I'm not sure how much. Also, would the elevator be exerting a force? I also know that gravity is a force but I think that's it.
 
  • #4


Ally385 said:
I know that the scale is exerting a force but I'm not sure how much.
Right, the scale exerts an upward force. The force it exerts is the reading on the scale.
Also, would the elevator be exerting a force?
No, not directly. (It exerts its force by pushing on the scale. All we care about are forces on the person, and the scale is the only thing touching the person.)
I also know that gravity is a force but I think that's it.
Good. Only two forces act. Set up an equation from Newton's 2nd law, then you can solve for the acceleration.

Can you figure out the person's mass?
 
  • #5


Ok so that would get you 828 N/ 9.8 m/s/s = 84.4898. Is that in kg? So that's the mass of the person so then do 919 N / 84.4898 = 10.88 which is your acceleration?

And then for the last part it would be 728/84.4898 = -8.62 the negative because it's slowing down. Negative acceleration. Correct?
 
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  • #6


I think it would be easier to use the difference in force 919- 828= 91 N. Since The 828 N was the weight of the person standing still, the 91 N must be the result of the upward acceleration of the elevator. NOW use "f= ma". What is m, the mass of the person?
 
  • #7


Ok so acceleration would be 9.29 m/s/s and then for the second part it would be -4.70! I get it thank you :D
 
  • #8


Ally385 said:
Ok so acceleration would be 9.29 m/s/s and then for the second part it would be -4.70! I get it thank you :D
You're off by a factor of 10. I suggest redoing them more carefully (especially the second part).

Don't skip steps. Write out the equation:
ƩF = ma
scale force - weight = ma
 
  • #9
Elevator Standing Still: Normal Force (reading on scale)= Weight of person = mg
The Normal force required is enough to balance the downward force created by the mass (person) wanting to accelerate downward at 9.8 m/s/s. (the scale/floor of elevator prevents them from plummeting to their death)

Elevator accelerating upward: Normal force(reading on scale)= mg (for the same reasons as stated above) + ma. with "a" being upward acceleration of the mass (person) caused by the scale/elevator floor. (F=ma) since the force required to cause the upward acceleration opposes gravity, (just like the force required to prevent the person from plummeting to their death)

Elevator accelerating downward: same theory acceleration upward but since acceleration is in the same direction as gravity, it reduces the Normal Force required to keep the mass from plummeting. (you can subtract a positive value or add a negative value but either way, the Normal Force (reading on the scale) is reduced.
 

1. What is the weight of the student on the bathroom scale in the elevator?

The weight of the student on the bathroom scale in the elevator is equal to their true weight. This is because the elevator is at rest and there is no acceleration or force acting on the student.

2. Will the weight of the student change as the elevator moves up or down?

No, the weight of the student will remain the same as long as the elevator is moving at a constant velocity. This is because the student's weight is determined by the force of gravity, which is constant on Earth.

3. Why does the bathroom scale show a different reading when the elevator is moving?

The bathroom scale may show a different reading when the elevator is moving because of the additional force of acceleration. As the elevator moves up or down, the scale will register a higher or lower reading due to the acceleration force acting on the student's body.

4. What would happen to the weight of the student if the elevator was in free fall?

If the elevator was in free fall, the weight of the student would be equal to zero. This is because there is no force of gravity acting on the student's body during free fall, and therefore the scale would register a weight of zero.

5. How does the altitude of the elevator affect the weight of the student?

The altitude of the elevator has no effect on the weight of the student. As long as the elevator is at rest or moving at a constant velocity, the weight of the student will remain the same regardless of the altitude of the elevator.

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