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

AI Thread Summary
The problem involves two masses, m1 (31.7 kg) and m2 (5.30 kg), connected by a string over a frictionless pulley, with a force of 216.9 N applied to m1 at an angle of 29.3 degrees. The coefficient of kinetic friction between m1 and the surface is 0.221, which affects the normal force and the net force acting on m1. The normal force was calculated to be 204.513 N, leading to an acceleration of m1 of 4.54 m/s². However, the tension in the string must be considered, as it affects the acceleration of m2, which is not equal to that of m1. The discussion emphasizes the need to account for the tension when determining the upward acceleration of m2.
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.

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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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