What is the upward acceleration of M2 in this system with given forces and mass?

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SUMMARY

The upward acceleration of mass m2 (5.30 kg) in the given system is determined by analyzing the forces acting on mass m1 (31.7 kg) and incorporating the effects of tension in the string. The normal force (Fn) for m1 is calculated as 204.513 N, and the acceleration of m1 is found to be 4.54 m/s². However, the acceleration of m2 must also account for the tension in the string, which affects the overall acceleration of the system. The correct approach requires applying Newton's second law to both masses simultaneously to find the accurate upward acceleration of m2.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Knowledge of forces acting on objects (normal force, tension)
  • Familiarity with kinetic friction and its coefficient
  • Ability to resolve forces into components (sine and cosine functions)
NEXT STEPS
  • Calculate the tension in the string connecting m1 and m2
  • Learn how to apply Newton's second law to multiple connected objects
  • Explore the effects of friction on acceleration in similar systems
  • Study pulley systems and their dynamics in physics
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Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of force analysis in connected mass systems.

ganondorf29
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Homework Statement


Mass m1=31.7 kg is on a horizontal surface, connected to mass m2= 5.30 kg by a light string as shown. The pulley has negligible mass and no friction. A force of 216.9 N acts on m1 at an angle of 29.3deg. The coefficient of kinetic friction between m1 and the surface is 0.221. Determine the upward acceleration of m2.

physicsprblm.jpg

Homework Equations


F=ma
Fn = mg-Fsin(theta)
Fcos(theta)-(uk)(Fn) = ma

The Attempt at a Solution


First I found the normal force of M1. Fn = mg-Fsin(theta). I found Fn to be 204.513 N. Next, I found the acceleration of M1 by using [Fcos(theta)-(uk)(Fn)] / m = a. I got ax to be 4.54 m/s^2. I assumed that the acceleration would be the same for M2 but its not.
 
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You forgot to consider the string tension acting on the block. (The accelerations of M1 and M2 must be the same--they are connected by a string.)
 

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