Calculating Tension in a String: Mass and Acceleration Relationship Explained

In summary, a sphere is accelerated upwards by a string and its speed increases. The tension in the string remains constant during that time.
  • #1
BuBbLeS01
602
0
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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  • #2
it would help if you cheak your textbook and tells us what you are.eg:(pri.sec.jc.poly)
(visit my blog!)
 
  • #3
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.
 
  • #4
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.
 
  • #5
I am using f=ma and a I am putting as positive is that not right?
 
  • #6
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?
 
  • #7
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?
 
  • #8
Doc Al said:
Nothing wrong with that, using up = +. What forces act on the mass?
the tension and gravity
 
  • #9
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!
 

1. How do you calculate tension in a string?

To calculate tension in a string, you need to know the mass of the object attached to the string and the acceleration it is experiencing. You can then use the formula T = m x a, where T represents tension, m represents mass, and a represents acceleration.

2. What is the relationship between mass and tension in a string?

The relationship between mass and tension in a string is directly proportional. This means that as the mass increases, the tension in the string will also increase. Similarly, as the mass decreases, the tension will decrease as well.

3. How does acceleration affect tension in a string?

Acceleration also has a direct relationship with tension in a string. As acceleration increases, tension will also increase. Conversely, if acceleration decreases, tension will decrease as well.

4. Can you have tension in a string without any mass attached to it?

No, tension in a string is caused by the weight of the object attached to it. Without any mass, there will be no tension in the string.

5. How can tension in a string be measured?

Tension in a string can be measured using a spring scale or a force meter. These tools can measure the force being applied to a string, which is equivalent to the tension in the string.

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