Problem on an atwood's machine given an upward acceleration

In summary, the conversation discusses finding the acceleration of each mass and the tension in the string in an Atwood's machine that is given an upward acceleration. The equations for the tensions and the effect of friction are also mentioned, with the mention that the problem becomes more difficult without values for the masses.
  • #1
mnlaguerta
1
0
The pulley in an atwood's machine is given an upward acceleration a. Find the acceleration of each mass and the tension in the string that connects them.

so my problem here is deriving the equation for the acceleration of both masses considering that the system was applied with an upward force. what will the upward acceleration do to the system? well, if the system wasn't given any upward acceleration i know that:

[tex]\sum[/tex]Fy1= T1-m1g=-m1a
[tex]\sum[/tex]Fy2= T2-m2g=m2a

are the tensions equal?
my professor didn't give us any values for the masses which make this problem even tougher for me. please help me. :cry:
 
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  • #2
mnlaguerta said:
are the tensions equal?

It depends on friction. Is there any friction in this task? If yes, tensions are not equal. What about masses? Are they among the data?
Considering acceleration, it seems it will be a-g. In your equations you just have to change g for g-a and a for b-a, where b is acceleration of each mass if the pulley is not given any acceleration. If you have masses, it is not a very difficult problem.
 
  • #3


The upward acceleration applied to the pulley in an Atwood's machine will affect the acceleration of both masses in the system. To determine the acceleration of each mass, we can use the equations of motion for each mass. The tension in the string connecting the masses will also be affected by the upward acceleration.

To start, we can consider the free body diagrams for each mass. For mass 1, the forces acting on it are the tension force (T1) and the force of gravity (m1g). For mass 2, the forces acting on it are the tension force (T2) and the force of gravity (m2g). Since the pulley is accelerating upward, there must be a net upward force acting on it, which we can denote as F. This force will be equal to the sum of the tensions in the string, so we can write it as F = T1 + T2.

Using Newton's second law (F=ma), we can set up the equations of motion for each mass:

For mass 1:
\sumFy1= T1-m1g=m1a1

For mass 2:
\sumFy2= T2-m2g=m2a2

Since the upward acceleration is the same for both masses, we can set a1 = a2 = a. Substituting this into the equations above, we get:

For mass 1:
T1-m1g=m1a

For mass 2:
T2-m2g=m2a

We now have two equations and two unknowns (T1 and T2), so we can solve for both tensions. To do this, we can use the fact that the net upward force acting on the pulley (F) must be equal to the sum of the tensions (T1 + T2). So we can write:

F = T1 + T2

Substituting in the equations for T1 and T2, we get:

F = (m1a + m2a) + (m1g + m2g)

Rearranging, we get:

F = (m1+m2)a + (m1+m2)g

Now, we can substitute this value for F into our equations for T1 and T2:

For mass 1:
T1-m1g=m1a
T1 = m1a + m1g - F

For mass 2
 

1. What is an Atwood's machine?

An Atwood's machine is a simple mechanical device used to study the principles of classical mechanics. It consists of two masses connected by a string over a pulley, and is commonly used to demonstrate the concept of acceleration due to gravity.

2. How does an upward acceleration affect an Atwood's machine?

An upward acceleration in an Atwood's machine will cause the heavier mass to move downward and the lighter mass to move upward. This is due to the difference in weight between the two masses, with the heavier mass experiencing a greater gravitational force and therefore accelerating faster.

3. How do you calculate the tension in the string of an Atwood's machine?

The tension in the string can be calculated using the formula T = (m1-m2)a, where T is the tension, m1 and m2 are the masses, and a is the acceleration. This assumes that the string is massless and there is no friction present.

4. What factors can affect the acceleration of an Atwood's machine?

The acceleration of an Atwood's machine can be affected by the difference in mass between the two masses, the tension in the string, and any external forces acting on the system (such as friction or air resistance).

5. How can an Atwood's machine be used in real-world applications?

An Atwood's machine can be used to study the principles of mechanics in a controlled and simplified environment. It can also be used to measure the acceleration due to gravity, and has been used in the past to test the efficiency of different types of pulleys and strings.

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