How to Determine the Upward Acceleration of a Mass in a Pulley System?

AI Thread Summary
To determine the upward acceleration of mass m2 in a pulley system, the problem involves applying Newton's second law to both masses, accounting for forces such as tension, friction, and the applied force. The tension in the string must be equal for both masses, and the friction force is calculated using the coefficient of kinetic friction and the normal force. The normal force is influenced by the weight of m1 and the vertical component of the applied force. It is crucial to recognize that the system is not in equilibrium, as both masses are accelerating. The correct upward acceleration of m2 is found to be 2.44 m/s².
delecticious
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Homework Statement


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Mass m1=26.1 kg is on a horizontal surface, connected to mass m2= 5.50 kg by a light string as shown. The pulley has negligible mass and no friction. A force of 197.7 N acts on m1 at an angle of 33.3 deg.
The coefficient of kinetic friction between m1 and the surface is 0.233. Determine the upward acceleration of m2.
2.44 m/s^2

Homework Equations


a1 = a2

T1 = T2

T1 = Fcos(theta) - Frictionforce

Friction force = uk(Normal Force)

Normal Force = weight - Fsin(theta)


The Attempt at a Solution



I'm actually looking at this problem again since I first did a week ago and I don't have the sheet I worked it out on with me right now, but using the equations I wrote above keeping in mind that T1=T2 I pretty much worked the whole thing out, however when I entered it into the online homework system I got it wrong no matter what I did I just couldn't get it. Can someone help me out with what I'm doing wrong? By the way I know what the answer is, but I just no how you would go about getting to it, I step-by-step run down through the problem would be helpful.
 
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delecticious said:
a1 = a2

T1 = T2
These are OK.

T1 = Fcos(theta) - Frictionforce
This assumes equilibrium, which is not the case here: the masses are accelerating. For each mass, apply Newton's 2nd law. You'll get two equations which you can solve together.

Friction force = uk(Normal Force)

Normal Force = weight - Fsin(theta)
OK.
 
Is the weight both masses added together? I have this same question with different numbers/masses.

is friction force the same as mass*acceleration = u*normal force?
 
lexi011 said:
Is the weight both masses added together? I have this same question with different numbers/masses.
No. Why would you add the weights together?
is friction force the same as mass*acceleration = u*normal force?
The friction force will equal μ*N. (But don't set it equal to mass*acceleration--other forces are acting.)
 

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