N's 2nd law: an eq'n for acceleration 'a'

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SUMMARY

The discussion centers on deriving a single equation for acceleration 'a' using two provided formulas: ma = mg - T and T = Ma. The user attempts to combine these equations but expresses uncertainty about their manipulation. The correct approach involves substituting T from the second equation into the first, leading to the equation mg - ma = Ma. This results in a clear expression for acceleration, defined as a = (mg - Ma) / m.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with basic algebraic manipulation
  • Knowledge of forces acting on objects (tension, gravity)
  • Experience with pulley systems in physics
NEXT STEPS
  • Study the derivation of equations of motion in physics
  • Learn about tension in pulley systems and its applications
  • Explore advanced topics in dynamics, including friction and net forces
  • Practice solving problems involving multiple masses and forces
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Students in physics courses, educators teaching mechanics, and anyone interested in understanding dynamics and forces in motion.

ms. confused
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Hello!

I was given two formulae for my Physics lab: ma=mg-T and T=Ma (using a pulley).

ma--> net force on small object (paper clip)
M--> larger mass (glider)
mg--> force of gravity
a--> acceleration
T--> tension of ribbon used

I'm supposed to combine the two equations to get one equation for acceleration. I thought about arranging them this way, but I think I'm wrong:

T=Ma (1)
T=mg-ma (2)
0 = -mg + (Ma+ma)

(the last part is difinitely messed up!)

Hope some can help me out! :confused:
 
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if T = Ma and T = mg - ma then mg - ma = Ma
 

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