What if check: Am I calculating tension wrong?

In summary, the conclusion of the discussion is that the acceleration of the mass m2 is equal to the gravitational force Fg.
  • #1
Callista
5
2

Homework Statement


Two objects are connected by a string that passes over a frictionless pulley, where m1<m2 and a1 and a2 are the magnitudes of the respective accelerations. Which mathematical statement is true regarding the magnitude of the acceleration a2 of the mass m2?
(a) a2<g
(b) a2>g
(c) a2=g
(d) a2<a1
(e) a2>a1

Homework Equations


F(net)=ma

The Attempt at a Solution


for m1:
F(net)=m1a
Fx=0
Fy=T-m1g=m1a1
##a1= \frac{T}{m1}-g##

for m2:
F(net)=m2a
Fx=0
Fy=-T+m2g=m2a2
##a2=g- \frac{T}{m2}<g##

Answer= (a)

While the book confirms my answer is right, I wanted to try applying my derived formulas to the situation where m1=5kg, and m2=10kg to see what the result would be. However, when I do this I run into a problem.

##a2=g- \frac{T}{m2}##
->##Fy=-T+m2g=m2a2##
->##T=m2g-m2a2##
->##a2=g- \frac{m2g-m2a2}{m2}##
->##a2=g- g+a2##
->##a2=a2##

A similar thing happens when I try to use the equation I derived for a1. What am I missing?
 
Last edited:
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  • #2
Callista said:
Fy=T-m1g=0
Why =0?
 
  • #3
haruspex said:
Why =0?
Sorry, looks like I mistyped that. I meant to say
->Fy=T-m1g=m1a1
->Fy=-T+m2g=m2a2
I've update my post to reflect it.

Upon reflection, I realize I was trying to use the same formula twice to solve for a new variable... Thanks for all the help.
 
Last edited:
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  • #4
You have two equations each one from applying Newton's 2nd law to each body
##T-m_1g=m_1a_1##
##m_2g-T=m_2a_2##

You have to solve for tension from the one equation and replace the tension into the other equation. If you solve for tension from one equation and replace it into the same equation it is a simple mathematical consequence that you will end up with conclusions of the form ##a_i=a_i##.
 
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Related to What if check: Am I calculating tension wrong?

1. What is tension and why is it important to calculate it accurately?

Tension is a force that is applied to an object, often in the form of a pulling or stretching force. It is important to calculate tension accurately because it can affect the stability and structural integrity of an object or system.

2. How do I calculate tension?

To calculate tension, you need to know the mass of the object, the acceleration due to gravity, and the angle of the force being applied. You can then use the formula T = mgcosθ, where T is tension, m is the mass, g is the acceleration due to gravity, and θ is the angle of the force.

3. What if my calculated tension seems too high or too low?

If your calculated tension seems too high or too low, it is possible that you made a mistake in your calculations or that there are other factors at play. Double check your calculations and make sure you are using the correct formula. If the issue persists, it is best to consult with a colleague or a mentor for assistance.

4. How do I know if I am calculating tension correctly?

To ensure that you are calculating tension correctly, it is important to double check your calculations and make sure you are using the correct formula. You can also compare your results to other sources or ask for feedback from a colleague or mentor.

5. Are there any common mistakes when calculating tension?

Yes, there are several common mistakes that can occur when calculating tension. Some of these include using the wrong formula, making a mistake in your calculations, or not taking into account all the factors that can affect tension. It is important to be thorough and double check your work to avoid these mistakes.

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