Determine the elevator's acceleration

y90x

1. 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.
2. Homework Equations
F=ma

3. The Attempt at a Solution
I know the acceleration is 0.152 m/s^2 upwards , I need help solving the problem
View attachment 215547
I drew a diagram , I’m no sure Im correct because I keep getting a number greater

Last edited:
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kuruman

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Draw a free body diagram, then apply the relevant equation that you posted.

y90x

Draw a free body diagram, then apply the relevant equation that you posted.
Would the rope have an impact though?

kuruman

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

y90x

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 ?

haruspex

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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.

kuruman

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You have the equation with the man as the system. However the tension is unknown. How are you going to find that?

y90x

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 ?

haruspex

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I’m no sure , I have two missing variables. Wouldn’t that mean to supplement a (acceleration) with F/M ?
See post #6.

y90x

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

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haruspex

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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.

y90x

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)

haruspex

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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.

y90x

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)

kuruman

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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.

y90x

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 ?

haruspex

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T - Mdg + Fn = Mda ?
Which way is the normal force acting on the dumb waiter?

SammyS

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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?

y90x

Which way is the normal force acting on the dumb waiter?
It’s going up , so shouldn’t it be added to tension

y90x

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 ?

kuruman

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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.

y90x

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 ?

kuruman

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• SammyS

y90x

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

kuruman

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You have two equations, one for the man and one for the dumbwaiter, and two unknowns, the acceleration and the tension.

"Determine the elevator's acceleration"

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