Calculating Acceleration of an Elevator with a Suspended Object: Explained

[Muteb]

The tension on a string from which?
The tension on a string from which a 4.0 kg object is suspended in an elevator is equal to 44.0 Newton.

What is the acceleration of the elevator?

Is this answer rigth

44 N - (4.0 kg X 9.8) = a (4.5 + 4) I think the 4.5 is mass of elevator and 4 the mass of the object which is suspended.

Acceleration = 0.57 m/s^2

 

[berkeman]

The mass of the elevator is not important. You are starting in the right direction. (4kg X 9/8 m/s^2) is the normal weight that would produce tension in the string if there were no vertical acceleration. The difference between this tension and the actual tension in the accelerating elevator is due to the elevator's acceleration. Please try writing the equation(s) again, being more careful to separate out the parts...

 

[dimpledur]

No, the left side of the equation is right, however, the right side is not. There is no way the mass of the elevator is 4.5, but regardless, that is irrelevant. For this question, you do not need to know the mass of the elevator, just the object suspended from the string.

 

[Muteb]

I can understand that
44 N - (4.0 kg X 9.8) = a X4
a= 1.2 m/s^2
is it ok now

 

[berkeman]

I can understand that
44 N - (4.0 kg X 9.8) = a X4
a= 1.2 m/s^2
is it ok now

So tell us in your own words why you think that is the right answer.

 

[Muteb]

I think that was not right. because I am asked to find the elevator's acceleration.

Mass of elevator is 44N / 9.8 = 4.5

44 N - (4.0 kg X 9.8) = a X 4.5
a = -1.1 m/s^2

 

[dimpledur]

You were right before, now it just seems you are becoming more confused. In this case, when the elevator accelerates, that which is in it, accelerates too.

 

[Muteb]

I am really confused.

44-(4X9.8)= 4 X a
a= 1.2 m/s^2 now I think that right because as you said the elevator has acceleration as the spring.

 

[dimpledur]

Yes, that is right, but do you understand why?

 

[Muteb]

Yes because the acceleration of the spring should be the same with the elevator.

is the direction right that the acceleration is +1.2 m/s^2 that means that the elevator accelerates up?

 

[PhanthomJay]

Yes because the acceleration of the spring should be the same with the elevator.

is the direction right that the acceleration is +1.2 m/s^2 that means that the elevator accelerates up?

Acceleration is always in the direction of the net force.
If the net force acts up on the object, then the object is accelerating up.