Meg N.

asked • 09/23/14

Solving for acceleration in terms of masses

W1-T=m1a              T-W2=m2a
 
Solve the problem for acceleration in terms of the masses and the acceleration due to gravity, find the function a(m1,m2,G).  If m1=4kg and m2=10kg, what is acceleration?  What is the tension in the string?

Bob A.

You are assuming we know what the diagram looks like.
We Do Not!
 
Is this a string over a pulley?
Is the pulley on the edge of a table?
Is the string trying to use a mass hanging to move a mass on the table?
Or are we talking about an Atwood's machine with 2 hanging masses?
Those are 2 typical problems - but we don't know which or even if yours is typical.
Is m1 or m2 the one hanging over a table?
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09/29/14

1 Expert Answer

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Byron S. answered • 10/01/14

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The weights of each mass is given by m*g, where g=9.8m/s2. We can eliminate T from your two equations by adding them together to get:
W1 - W2 = m1a + m2a
 
Substituting mg for each weight, we have
m1g - m2g = m1a + m2a
(m1 - m2)g = (m1 + m2) a
 
Divide to solve for a.
 
Now to solve the specific case, plug in the given values for m1 and m2 to find a, then substitute these into one of the original force equations to solve for T.
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