Calculating Elevator Acceleration: Solve for F=ma

In summary, when a person stands on a bathroom scale in a motionless elevator and the elevator begins to move, the scale briefly reads 1.05 times the person's regular weight. To calculate the magnitude and direction of the acceleration of the elevator, the equation ΣF=9.8m-9.8(1.05m+m) can be used, where ΣF is the difference between the force of gravity and the force of tension acting on the person. The resulting acceleration is directly related to the forces acting on the elevator and the person inside it. By simplifying the equation, the acceleration can be found by equating it to "ma".
  • #1
Jeff Nilsson
2
0

Homework Statement


A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads 1.05 times the persons regular weight. Calculate the magnitude and direction of the acceleration of the elevator.

Homework Equations


F=ma

The Attempt at a Solution


Fg = 9.8m
ΣF = 9.8(1.05m + m)
0 = 1.05m + m
-m = 1.05m
-1 = 1.05

I know that's not true but I don't really know how to set up the problem
 
Physics news on Phys.org
  • #2
Jeff Nilsson said:
ΣF = 9.8(1.05m + m)
Please explain your reasoning behind this equation.
What forces act on the person during the acceleration?
What acceleration results?
 
  • #3
haruspex said:
Please explain your reasoning behind this equation.
What forces act on the person during the acceleration?
What acceleration results?

Actually the equation would be ΣF=9.8m-9.8(1.05m+m) according to my logic
but ΣF in this case is the difference between the force of gravity and the force of tension
the 9.8m part is to find the force of gravity on the person in the motionless elevator and the 9.8(1.05m+m) part is to find the force acting on the person when the elevator starts accelerating upward
to find ΣF you subtract the force of gravity from the fore of tension since it is larger
my physics teacher said that sometimes if you set up equations without numbers the variables will cancel out so I tried that and nothing cancels
The only number the problem gives me is 1.05 times the original weight when the elevator starts accelerating
and since the person is inside the elevator it's a system and the forces acting on the elevator vary directly with the forces acting on the person
 
  • #4
Jeff Nilsson said:
the 9.8(1.05m+m) part is to find the force acting on the person when the elevator starts accelerating upward
Maybe I misunderstand your notation, but that appears to reduce to 9.8(2.05)m. Is that what you meant?

Jeff Nilsson said:
nothing cancels
It will. When you have corrected your "9.8(1.05m+m)" and written it in simplest form, equate it to "ma", as in ΣF=ma.
 

1. How do you calculate elevator acceleration?

To calculate elevator acceleration, you need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for calculating acceleration is a = F/m, where "a" is the acceleration, "F" is the net force, and "m" is the mass of the elevator.

2. What is the formula for solving for F=ma?

The formula for solving for F=ma is F = m * a, where "F" is the net force, "m" is the mass, and "a" is the acceleration. This formula is derived from Newton's second law of motion, which relates force, mass, and acceleration.

3. How do you determine the mass of the elevator?

To determine the mass of the elevator, you can use a scale to measure the weight of the elevator. Then, use the formula F = m * g, where "F" is the weight, "m" is the mass, and "g" is the acceleration due to gravity (9.8 m/s^2). Rearrange the formula to solve for "m" and you will have the mass of the elevator.

4. What units should be used for acceleration when solving for F=ma?

The units for acceleration when solving for F=ma should be meters per second squared (m/s^2). This is the standard unit of measurement for acceleration in the metric system.

5. Can you use this formula to calculate acceleration for any elevator?

Yes, this formula can be used to calculate acceleration for any elevator as long as the net force and mass are known. It is important to note that the formula assumes the elevator is moving in a straight line and at a constant speed.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
793
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
992
  • Introductory Physics Homework Help
Replies
5
Views
941
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
33
Views
3K
  • Introductory Physics Homework Help
Replies
8
Views
3K
Back
Top