Calculating Tension in a String: Mass and Acceleration Relationship Explained

[BuBbLeS01]

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.

 

[kaisxuans]

it would help if you cheak your textbook and tells us what you are.eg:(pri.sec.jc.poly)
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[Doc Al]

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.

 

[arildno]

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.

 

[BuBbLeS01]

I am using f=ma and a I am putting as positive is that not right?

 

[arildno]

To say that a is positive is perfectly valid.

Now, f is the sum of forces acting upon your mass.
What individual forces is f the sum of?

 

[Doc Al]

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?

 

[BuBbLeS01]

Nothing wrong with that, using up = +. What forces act on the mass?

the tension and gravity

 

[Doc Al]

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.

 

[BuBbLeS01]

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.

 

[arildno]

So, weight is a "minus" force, agreed?

Set up Newton's second law!

 

[Doc Al]

gravity acts down (g=9.8) and T acts up.

Good. Set up an equation per Newton's 2nd law and solve for T.

 

[BuBbLeS01]

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?

 

[Doc Al]

Fnet=ma
T-g=ma
T=(ma)+g
is that right?

Almost. g is the acceleration due to gravity, but weight is mg.

 

[BuBbLeS01]

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.

 

[Doc Al]

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!

 

[BuBbLeS01]

You've almost got it. Keep going!

I am getting an answer of 29.4151 N...

 

[Doc Al]

I am getting an answer of 29.4151 N...

Sounds about right. Round off your answer to a reasonable number of significant figures.

 

[BuBbLeS01]

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?

 

[BuBbLeS01]

Would you use Vf = Vo + at to find the acceleration?

 

[BuBbLeS01]

Oh nevermind I got it!