Determine the elevator's acceleration

Click For Summary

Homework Help Overview

The problem involves an 82 kg man inside a 40-kg dumbwaiter, where the man pulls down on a rope, and the scale reads 209 N. The objective is to determine the elevator's acceleration, which relates to concepts in dynamics and forces.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss drawing free body diagrams and applying relevant equations. There is uncertainty about the impact of the rope and the forces acting on both the man and the dumbwaiter. Questions arise regarding the correct interpretation of forces, such as tension and normal force, and how they relate to the system's acceleration.

Discussion Status

Participants are actively engaging with the problem, exploring different interpretations of forces and equations. Some have offered guidance on considering the system as a whole, while others are questioning the assumptions made about the forces involved. There is a recognition of the need to account for multiple variables and forces in the equations.

Contextual Notes

There is a focus on Newton's laws and the relationship between forces exerted by the man and the dumbwaiter. Participants note the importance of distinguishing between the forces acting on the man and those acting on the dumbwaiter, as well as the implications of the system's acceleration on the normal force measured by the scale.

y90x
Messages
47
Reaction score
0

Homework Statement



An 82 kg man inside a 40-kg dumb-waiter pulls down on the rope. At that moment the scale on which he is standing reads 209 N. Determine the elevator's acceleration.

Homework Equations


F=ma

The Attempt at a Solution


I know the acceleration is 0.152 m/s^2 upwards , I need help solving the problem
https://www.physicsforums.com/attachments/215547
I drew a diagram , I’m no sure I am correct because I keep getting a number greater
 
Last edited:
Physics news on Phys.org
Draw a free body diagram, then apply the relevant equation that you posted.
 
kuruman said:
Draw a free body diagram, then apply the relevant equation that you posted.

Would the rope have an impact though?
 
y90x said:
Would the rope have an impact though?
What do you think? Would the man be able to raise himself without it?
 
kuruman said:
What do you think? Would the man be able to raise himself without it?

Fn=209N (the scale reading)
Fg=mg
=(82kg)(9.8) = 803.6 N

And the force exerted on the rope is T
So the formula would be,

(Fn +T)-Fg=ma

Am I wrong or missing something ?
 
y90x said:
missing something ?
That's just for the man, right?
What about the equation for the dumb waiter? Make sure to use a different variable for the mass.
 
You have the equation with the man as the system. However the tension is unknown. How are you going to find that?
 
kuruman said:
You have the equation with the man as the system. However the tension is unknown. How are you going to find that?

I’m no sure , I have two missing variables. Wouldn’t that mean to supplement a (acceleration) with F/M ?
 
y90x said:
I’m no sure , I have two missing variables. Wouldn’t that mean to supplement a (acceleration) with F/M ?
See post #6.
 
  • #10
haruspex said:
That's just for the man, right?
What about the equation for the dumb waiter? Make sure to use a different variable for the mass.

Image1511565636.718284.jpg

Would this be all the forces ? Or would the dumb waiter exert a normal force as well
 

Attachments

  • Image1511565636.718284.jpg
    Image1511565636.718284.jpg
    5.3 KB · Views: 1,090
  • #11
y90x said:
View attachment 215554
Would this be all the forces ? Or would the dumb waiter exert a normal force as well
You have ΣF=ma equation for the man. Your second one can be either for the dumb waiter only or for the man+dumb waiter combination. Your choice.
If for the dumb waiter, what force does the man exert on it? Remember Newton's laws.
If for the combination, ignore forces between the man and the dumb waiter since they are internal to the system, but be careful about the force the rope exerts on the combination.
 
  • #12
haruspex said:
You have ΣF=ma equation for the man. Your second one can be either for the dumb waiter only or for the man+dumb waiter combination. Your choice.
If for the dumb waiter, what force does the man exert on it? Remember Newton's laws.
If for the combination, ignore forces between the man and the dumb waiter since they are internal to the system, but be careful about the force the rope exerts on the combination.

If I were to chose only the dumb waiter c wouldn’t it be the gravitational force going down and the tension ?
So it’ll be
Fnet=ma
T-Md=Md(a)
 
  • #13
y90x said:
If I were to chose only the dumb waiter c wouldn’t it be the gravitational force going down and the tension ?
So it’ll be
Fnet=ma
T-Md=Md(a)
You left out g, and another force. As I wrote, remember Newton's laws.
 
  • #14
haruspex said:
You left out g, and another force. As I wrote, remember Newton's laws.

Oh yes !
Wouldn’t it be the man’s force being exerted down on the elevator ?

T- Md•g - M•g = a(Md+M)
 
  • #15
y90x said:
T- Md•g - M•g = a(Md+M)
In Fnet = ma, m is the mass of the system. Your system is the dumbwaiter, so what quantity should multiply a?
Also on the left side you have M⋅g. That's the force that the Earth exerts on the man, however neither the Earth nor the man are part of this system. The force exerted by the man on the dumbwaiter is not his weight. What is that force? As @haruspex wrote, remember Newton's Laws.
 
  • #16
kuruman said:
In Fnet = ma, m is the mass of the system. Your system is the dumbwaiter, so what quantity should multiply a?
Also on the left side you have M⋅g. That's the force that the Earth exerts on the man, however neither the Earth nor the man are part of this system. The force exerted by the man on the dumbwaiter is not his weight. What is that force? As @haruspex wrote, remember Newton's Laws.

So you would multiply a by 40? The mass of the dumbwaiter . So then the missing force would be the normal force in which the scale reads ?

T - Mdg + Fn = Mda ?
Since the man isn’t part of the system , his mass or weigh shouldn’t be included ?
 
  • #17
y90x said:
T - Mdg + Fn = Mda ?
Which way is the normal force acting on the dumb waiter?
 
  • #18
y90x said:
Oh yes !
Wouldn’t it be the man’s force being exerted down on the elevator ?
Yes.
T- Md•g - M•g = a(Md+M)
However, the man’s force being exerted down on the elevator isn't mg in this case.

What does Newton's third law say about the force the man exerts on the elevator as compared with the force the elevator exerts on the man?
 
  • #19
haruspex said:
Which way is the normal force acting on the dumb waiter?

It’s going up , so shouldn’t it be added to tension
 
  • #20
SammyS said:
Yes.

However, the man’s force being exerted down on the elevator isn't mg in this case.

What does Newton's third law say about the force the man exerts on the elevator as compared with the force the elevator exerts on the man?

That they should be equal but since the elevator is accelerating wouldn’t that make his weight seen heavier or lighter depending the speed it’s going ?
 
  • #21
y90x said:
That they should be equal but since the elevator is accelerating wouldn’t that make his weight seen heavier or lighter depending the speed it’s going ?
No. The weight is the force Mmang with which the Earth attracts the man. What changes is the normal force exerted by the scale on the man that always adapts itself to provide the observed acceleration. The scale measures the normal exerted on its surface. Just push down on a scale with your hand to convince yourself that it is not displaying your weight.
 
  • #22
kuruman said:
No. The weight is the force Mmang with which the Earth attracts the man. What changes is the normal force exerted by the scale on the man that always adapts itself to provide the observed acceleration. The scale measures the normal exerted on its surface. Just push down on a scale with your hand to convince yourself that it is not displaying your weight.

Oh, I see
So then it’ll be
T-209N-40g=40a ?
 
  • #23
y90x said:
So then it’ll be
T-209N-40g=40a ?
It'll be that.
 
  • Like
Likes   Reactions: SammyS
  • #24
kuruman said:
It'll be that.

But tension is still unknown, to solve it would it be

T - 82g = 209N because the elevator is going upwards, or
82g-T =209N
 
  • #25
You have two equations, one for the man and one for the dumbwaiter, and two unknowns, the acceleration and the tension.
 
  • #26
kuruman said:
You have two equations, one for the man and one for the dumbwaiter, and two unknowns, the acceleration and the tension.

So how do you find tension ?
 
  • #28
y90x said:
It’s going up , so shouldn’t it be added to tension
The normal force between the man and the dumb waiter (we can ignore the scale since that is considered massless, so just transmits the force straight through) must be up on one and down on the other. Does it act down on the man and up on the dumb waiter or the other way around?
 
  • #29
haruspex said:
The normal force between the man and the dumb waiter (we can ignore the scale since that is considered massless, so just transmits the force straight through) must be up on one and down on the other. Does it act down on the man and up on the dumb waiter or the other way around?

Wouldn’t it be the other way around ? Up on the man and down on the dumbwaiter ?
 
  • #30
Up on the man and down on the elevator is correct. Your equation in post #22 is also correct. Where does your equation in post #24 come from?
 

Similar threads

Mechanics: Elevator Accelerating Downward
  • · Replies 10 ·
Replies
10
Views
4K
Calculate elevator acceleration using mass
  • · Replies 9 ·
Replies
9
Views
4K
Calculating Elevator Acceleration: Solve for F=ma
  • · Replies 3 ·
Replies
3
Views
2K
Elevator Problem: Determining Scale Reading for a Moving Object
  • · Replies 5 ·
Replies
5
Views
2K
Elevator Motion and Bathroom Scale Readings
  • · Replies 2 ·
Replies
2
Views
2K
Acceleration of Body in Elevator & Earth with 0.5g Rise
  • · Replies 12 ·
Replies
12
Views
2K
Forces and Elevators: Free-Body Diagrams and Calculations
  • · Replies 9 ·
Replies
9
Views
7K
Comapring acceleration of person in elevator
  • · Replies 5 ·
Replies
5
Views
1K
Forces, elevator, acceleration -- I have the answer, just explain it....
  • · Replies 2 ·
Replies
2
Views
12K
Action-Reaction Forces on an Elevator
  • · Replies 5 ·
Replies
5
Views
3K