Atwood Machine, two masses + two pulleys (w/ mass)

In summary, the Atwood machine consists of two wheels with masses concentrated at the rims, a hanging mass on each side, and an unknown tension. By setting up equations for the sum of torques and forces, the acceleration can be solved for using substitution. The final equation for acceleration is a = (g(m3 - m4)) / (m1 + m2 + m3 + m4).
  • #1
destrow111
2
0

Homework Statement


An Atwood machine is constructed using two
wheels (with the masses concentrated at the
rims). The left wheel (m1) has a mass of 2.1 kg and
radius 21.44 cm. The right wheel (m2) has a mass
of 2.8 kg and radius 33.94 cm. The hanging
mass on the left (m3) is 1.53 kg and on the right (m4)
1.13 kg.



Homework Equations


Sum of Torque1= (m3)g(r1) - T(r1) = (m1)(r1)a
Sum of Torque2= T(r2) - (m4)g(r2) = (m2)(r2)a


The Attempt at a Solution


used subsitution to solve for a...
a = ((m3)g - (m4)g) / ((m1) + (m2))
 
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  • #2
welcome to pf!

hi destrow111! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
destrow111 said:
Sum of Torque1= (m3)g(r1) - T(r1) = (m1)(r1)a
Sum of Torque2= T(r2) - (m4)g(r2) = (m2)(r2)a

i'm not sure what the set-up is, but looking at those two equations, if T is an unknown, then you need to eliminate T …

how would you do that? :smile:​
 
  • #3


I actually figured it out!

there were actually three different tensions so i added sum of forces equations for each of the masses then subsituted a couple times until acceleration was the only unknown!

ended up being a = (g(m3 - m4)) / (m1 + m2 + m3 + m4)
 

Related to Atwood Machine, two masses + two pulleys (w/ mass)

1. How does an Atwood Machine work?

The Atwood Machine is a simple device that demonstrates the laws of motion and conservation of energy. It consists of two masses connected by a string that runs over two pulleys. The mass on one side of the string is greater than the mass on the other side, causing an imbalance in forces and resulting in the movement of the masses.

2. What are the components of an Atwood Machine?

An Atwood Machine consists of two masses, two pulleys, and a string. The two masses are connected by the string, which runs over the two pulleys. The pulleys are typically attached to a fixed support, and the masses can move freely up and down.

3. How does an Atwood Machine demonstrate Newton's laws of motion?

The Atwood Machine demonstrates Newton's laws of motion in several ways. Firstly, it shows the first law of motion, which states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. In this case, the external force is the imbalance in the masses. Secondly, it demonstrates the second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Lastly, it shows the third law of motion, which states that for every action, there is an equal and opposite reaction. In the Atwood Machine, the masses are pulling on each other with equal and opposite forces through the string.

4. How does the mass of the pulleys affect the motion of an Atwood Machine?

The mass of the pulleys has a minimal effect on the motion of an Atwood Machine. The pulleys themselves do not contribute to the forces acting on the masses, so their mass does not affect the overall motion. However, the mass of the pulleys may affect the friction and inertia of the system, which can impact the accuracy of the results.

5. How does the Atwood Machine demonstrate conservation of energy?

The Atwood Machine demonstrates conservation of energy by showing that the total energy of the system remains constant. As the masses move, they exchange potential and kinetic energy, but the sum of these energies remains the same. This is because the work done by the forces acting on the masses is equal to the change in kinetic energy, and the potential energy is related to the height of the masses, which remains constant as they move up and down.

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