Calculating Tension in a String: Mass and Acceleration Relationship Explained

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Homework Help Overview

The discussion revolves around calculating the tension in a string supporting a mass that is accelerating upwards. The original poster presents a scenario involving a 2.21 kg mass with an upward acceleration of 3.50 m/s² and seeks guidance on how to approach the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss identifying forces acting on the mass, including tension and gravity, and applying Newton's second law. There are questions about the correct sign conventions for forces and accelerations, as well as how to set up equations based on these forces.

Discussion Status

Participants are actively engaging in the problem, with some providing hints and guidance on how to set up equations. There is recognition of the need to clarify the roles of different forces and how they contribute to the net force acting on the mass. The conversation includes attempts to derive the tension in the string, with some participants expressing frustration over the process.

Contextual Notes

There are indications of confusion regarding the application of Newton's second law and the definitions of forces involved, particularly the distinction between weight and mass. The original poster expresses frustration about their understanding of the problem.

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A 2.21 kg mass is suspended from a string which is pulled upward. The mass accelerates upwards with an acceleration of 3.50 m/s2. What is the tension in the string

I don't have anything yet because I don't know where to start or what equation to use.
 
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it would help if you cheak your textbook and tells us what you are.eg:(pri.sec.jc.poly)
(visit my blog!)
 
BuBbLeS01 said:
I don't have anything yet because I don't know where to start or what equation to use.
Identify the forces acting on the mass (draw a diagram with forces labeled) and apply Newton's 2nd law.
 
Hint:
First choose whether "upwards" should be the positive direction or negative.
Then, according to this choice, determine the sign of the known force(s) and accelerations.

The correct sign for the unknown force will then appear out of thin air when you have formulated the problem correctly.
 
I am using f=ma and a I am putting as positive is that not right?
 
To say that a is positive is perfectly valid. :smile:

Now, f is the sum of forces acting upon your mass.
What individual forces is f the sum of?
 
BuBbLeS01 said:
I am using f=ma and a I am putting as positive is that not right?
Nothing wrong with that, using up = +. What forces act on the mass?
 
Doc Al said:
Nothing wrong with that, using up = +. What forces act on the mass?
the tension and gravity
 
BuBbLeS01 said:
the tension and gravity
Good. Which way do they act? What's the force of gravity equal to? Call the tension "T" and add them up.
 
  • #10
Doc Al said:
Good. Which way do they act? What's the force of gravity equal to? Call the tension "T" and add them up.
gravity acts down (g=9.8) and T acts up.
 
  • #11
So, weight is a "minus" force, agreed?

Set up Newton's second law!
 
  • #12
BuBbLeS01 said:
gravity acts down (g=9.8) and T acts up.
Good. Set up an equation per Newton's 2nd law and solve for T.
 
  • #13
Doc Al said:
Good. Set up an equation per Newton's 2nd law and solve for T.
Fnet=ma
T-g=ma
T=(ma)+g
is that right?
 
  • #14
BuBbLeS01 said:
Fnet=ma
T-g=ma
T=(ma)+g
is that right?
Almost. g is the acceleration due to gravity, but weight is mg.
 
  • #15
Doc Al said:
Almost. g is the acceleration due to gravity, but weight is mg.
Okay so its weight that is the force acting down? So T=(ma) + w...I am sorry this question is simple and I am just not getting it and I am so frustrated right now.
 
  • #16
BuBbLeS01 said:
Okay so its weight that is the force acting down? So T=(ma) + w...I am sorry this question is simple and I am just not getting it and I am so frustrated right now.
You've almost got it. Keep going!
 
  • #17
Doc Al said:
You've almost got it. Keep going!
I am getting an answer of 29.4151 N...
 
  • #18
BuBbLeS01 said:
I am getting an answer of 29.4151 N...
Sounds about right. Round off your answer to a reasonable number of significant figures.
 
  • #19
Thank you so much! Another question though for a problem like this...

A sphere of mass of 1.39 kg is accelerated upwards by a string to which the sphere is attached. Its speed increases from 3.01 m/s to 4.81 m/s in a time of 2.28 s. Calculate the tension in the string, assuming that the tension remains constant during that time.

How do you incorporate the speed?
 
  • #20
Would you use Vf = Vo + at to find the acceleration?
 
  • #21
Oh nevermind I got it!
 

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