Solving Mass m2 Acceleration on a 30° Slope

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SUMMARY

The discussion focuses on solving the dynamics of mass m2 on a 30° slope connected to mass m1 via a frictionless pulley. The correct scalar equation for mass m2 is derived as FT - m2g sin(30°) = m2a, where FT represents the tension in the string, g is the acceleration due to gravity, and a is the acceleration of mass m2. The initial attempt incorrectly applied the forces, leading to confusion about the net unbalanced forces acting on m2.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of trigonometric functions, specifically sine (sohcahtoa)
  • Familiarity with the concepts of tension in strings and forces on inclined planes
  • Basic understanding of gravitational acceleration (g)
NEXT STEPS
  • Review the derivation of forces on inclined planes in classical mechanics
  • Study the application of Newton's laws in systems involving pulleys
  • Learn about the effects of friction on inclined planes and how it alters the equations
  • Explore advanced problems involving multiple masses and pulleys for deeper understanding
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of dynamics involving inclined planes and pulleys.

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Homework Statement


A mass, m2, on a 30^{o} slope is connected to another mass, m1, by a light string that passes over a frictionless pulley, as shown. The two masses are equal, the slope is smooth, and the acceleration due to gravity is g.
What is the scalar equation for mass m2, that correctly shows the relationship between the acceleration, a, of the mass and the tension in the string, FT?

http://img220.imageshack.us/img220/4884/inclinexx4.png​

Homework Equations


F = ma
sohcahtoa

The Attempt at a Solution


I got sin 30^{o} = m_{1}g - FT/m_{2}a - m_{2}g. However, this is wrong. The answer is supposed to be FT - m2g sin30^{o} = m2a.

Can someone show me where I went wrong please?
 
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Physics news on Phys.org
What two unbalanced forces are on m2?

what is the acceleration of m2 due to the net unbalanced force on m2?
 

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