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

In summary, the problem involves two masses, m1 = 26.1 kg and m2 = 5.50 kg, connected by a light string over a pulley with negligible mass and no friction. A force of 197.7 N is applied to m1 at an angle of 33.3 degrees, and the coefficient of kinetic friction between m1 and the horizontal surface is 0.233. The goal is to determine the upward acceleration of m2, which is found to be 2.44 m/s^2. The solution involves setting up two equations using Newton's 2nd law for each mass and solving for the unknown acceleration.
  • #1
delecticious
65
0

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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  • #2
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.
 
  • #3
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?
 
  • #4
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.)
 

1. What is a pulley system?

A pulley system is a simple machine that uses a rope or belt wrapped around a wheel to change the direction of a force. It allows for easier lifting or lowering of objects by distributing the weight across multiple ropes and pulleys.

2. How does a pulley system work?

A pulley system works by using the concept of mechanical advantage, where the effort needed to lift an object is less than the weight of the object itself. As the rope is pulled, the pulley redirects the force to lift the object in the desired direction.

3. What are the types of pulley systems?

There are three types of pulley systems: fixed, movable, and compound. A fixed pulley has a stationary axle and only changes the direction of the force. A movable pulley has a movable axle and reduces the effort needed to lift an object. A compound pulley is a combination of fixed and movable pulleys.

4. What factors affect the efficiency of a pulley system?

The efficiency of a pulley system is affected by the number of pulleys used, the type of pulley system, and the friction between the pulley and the rope. In general, the more pulleys used, the higher the mechanical advantage and the more efficient the system.

5. How can a pulley system be used in real-life applications?

A pulley system has many practical applications, such as elevators, cranes, and flagpoles. It is also commonly used in exercise equipment, window blinds, and clotheslines. The use of pulley systems allows for easier and more efficient lifting and lowering of heavy objects.

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