Calculating Tension in Atwood Machine

In summary, the conversation discusses the calculation of tension in an Atwood machine and the use of a curved coordinate axis for treating connected objects as a system. The first step involves using the overall acceleration to find individual internal forces, while the second step uses either of two equations to calculate net forces for each object. The first equation is derived from the latter two equations and accounts for negative acceleration for T2 and positive acceleration for T1. The use of the curved axis in the second step is unclear.
  • #1
Kalibasa
21
0

Homework Statement



I'm looking at how to calculate the tension in the ropes in an Atwood machine (two masses hanging on either side of a pulley, with mass 2 on the right side). We were told, for connected objects, that it was easiest to treat the two objects as a system and use a curved coordinate axis; then we were supposed to use this overall acceleration to find individual internal forces in a second step.


Homework Equations



The first step is ay= (m2-m1)g/(m1+m2)

But then in the second step he's suddenly giving us either of these equations to use:
Fnet2y= T-m2g= m2 (-ay)
Fnet1y= T-m1g=m1 (+ay)


The Attempt at a Solution



ay is negative for T2 and positive for T1. Does this mean that we're no longer using the curved axis in the second step?
 
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  • #2


i'm not really familiar with this 'curved axis' thing, but actually ur first equation is derived from the latter two
 
  • #3


I would first clarify the definitions and variables being used in this problem. It appears that the homework statement is referring to an experiment involving an Atwood machine, which is a simple mechanical device used to demonstrate the principles of acceleration and tension in a system of connected objects. The two masses hanging on either side of the pulley are referred to as m1 and m2, with m2 being on the right side. The homework equations provided include the acceleration of the system (ay) and the net forces acting on each mass (Fnet2y and Fnet1y).

In order to calculate the tension in the ropes, we must first understand how the system is moving. The equation ay= (m2-m1)g/(m1+m2) represents the overall acceleration of the system, which is determined by the difference in masses on either side of the pulley. This equation is used to find the net force acting on the system, which is necessary for calculating the tension in the ropes.

The second step, as described in the homework statement, involves using the overall acceleration to find individual internal forces. This is where the equations Fnet2y= T-m2g and Fnet1y= T-m1g come into play. These equations are based on Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force on each mass is equal to the tension in the rope minus the force of gravity acting on the mass.

It is important to note that the negative and positive signs in these equations represent the direction of the forces. In this case, the negative sign for T2 indicates that the tension in the rope is acting in the opposite direction of the acceleration, while the positive sign for T1 indicates that the tension is acting in the same direction as the acceleration.

To answer the question posed in the attempt at a solution, the use of a curved coordinate axis is still applicable in the second step. The equations Fnet2y= T-m2g and Fnet1y= T-m1g are simply a different way of representing the net forces acting on each mass, and do not change the overall approach of treating the two objects as a system and using the overall acceleration to find individual forces.

In conclusion, calculating the tension in an Atwood machine involves understanding the overall acceleration of the system and using it to find individual internal
 

What is an Atwood machine?

An Atwood machine is a simple mechanical device used to study the effects of gravity on two masses connected by a string or rope. It consists of a pulley, a string, and two masses of different weights.

How do you calculate tension in an Atwood machine?

The formula for calculating tension in an Atwood machine is T = (m1 - m2)g, where T is the tension in the string, m1 and m2 are the masses of the two objects, and g is the acceleration due to gravity.

What is the significance of calculating tension in an Atwood machine?

Calculating tension in an Atwood machine helps us understand the relationship between the masses and the force of gravity acting on them. It also allows us to analyze the motion and acceleration of the masses in the system.

What factors can affect the tension in an Atwood machine?

The tension in an Atwood machine can be affected by the masses of the objects, the length and angle of the string, and any external forces acting on the system, such as friction or air resistance.

How can tension in an Atwood machine be used in real-world applications?

Tension in an Atwood machine can be used in various real-world applications, such as elevators, cranes, and other lifting mechanisms. It is also used in physics experiments to study the principles of motion and gravity.

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