Pulley on an inclined plane

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SUMMARY

The discussion focuses on a frictionless pulley system connecting two masses, where one mass is positioned on a frictionless inclined plane at angle θ. The system has a mechanical advantage of 2, meaning that if mass m1 moves 1 meter, mass m2 moves only 0.5 meters. The equations governing the system are ΣF1 = m1a1 = m1g - T and ΣF2 = m2a2 = T - m2gsinθ. The acceleration of each mass and the tension in the rope can be derived from these equations, taking into account the mechanical advantage.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with the concept of mechanical advantage
  • Knowledge of trigonometric functions related to angles
  • Basic principles of pulley systems
NEXT STEPS
  • Study the derivation of acceleration in pulley systems with mechanical advantages
  • Learn about the effects of friction on pulley systems
  • Explore advanced topics in dynamics, such as non-inertial reference frames
  • Investigate real-world applications of pulley systems in engineering
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Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the dynamics of pulley systems and inclined planes.

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Homework Statement



A frictionless pulley connects 2 masses, one of which is on a frictionless inclined plane at angle θ, as shown in the diagram. The pulley system is set up so it has a mechanical advantage of 2 (so that if m1 moves 1 meter, m2 will move only 0.5 meters). Find equations that give the acceleration of each mass as well as the tension in the rope in terms of m1, m2, θ, and g.

Homework Equations



T=tension in the rope, subscripts indicate which mass the variable is referring to

ΣF1=m1a1=m1g-T
ΣF2=m2a2=T-m2gsinθ

The Attempt at a Solution



This problem is easy if it is a simple pully, since both accelerate at the same rate of a=g*(m1-m2sinθ)/(m1+m2). To get this you just have to add the above two equations and solve for a. But since there is a mechanical advantage of 2, m1 will accelerate twice as fast as m2, and thus you cannot simply add the equations to find the acceleration. I am not quite sure how to approach this problem, and any help would be appreciated.
 

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