Atwood Machine: Acceleration of m1

In summary, the problem involves three objects with masses m1 = 35.1 kg, m2 = 16.8 kg, and m3 = 10.5 kg hanging from ropes over pulleys. The goal is to find the acceleration of m1, with negative numbers representing downward motion and positive numbers representing upward motion. The equations used are F=ma and a=(m1-m2)g/(m1+m2). By setting up equations for the forces on m1 and expressing the tensions in terms of m1, m2, g, and a, a system of three equations and three unknowns is created, allowing for the solution of T1, T2, and a.
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Homework Statement


Three objects with masses m1 = 35.1 kg, m2 = 16.8 kg, and m3 = 10.5 kg are hanging from ropes that are redirected over pulleys. What is the acceleration of m1? Negative numbers for downward, and positive numbers for upward, please.


Homework Equations


F=ma
a=(m1-m2)g/(m1+m2)


The Attempt at a Solution


So I started the problem by saying that m1*g-(T1+T2)=m2*g+m3*g (T1 connects m2 and m1, T2 connects m3 and m1)
And T1=m2*a-m2g and T2=m3*g-m3*g. and substituted in for T1 and T2. Am I heading in the right direction?
 

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  • #2
thatguy101 said:

Homework Statement


Three objects with masses m1 = 35.1 kg, m2 = 16.8 kg, and m3 = 10.5 kg are hanging from ropes that are redirected over pulleys. What is the acceleration of m1? Negative numbers for downward, and positive numbers for upward, please.


Homework Equations


F=ma
a=(m1-m2)g/(m1+m2)


The Attempt at a Solution


So I started the problem by saying that m1*g-(T1+T2)=m2*g+m3*g (T1 connects m2 and m1, T2 connects m3 and m1)
And T1=m2*a-m2g and T2=m3*g-m3*g. and substituted in for T1 and T2. Am I heading in the right direction?

Your reasoning is not clear. The force on m1 is m1g minus the tensions. What is that equal to? Use that as your first equation.

Express the tensions in terms of m1, m2, g and a. You should get two equations.

That will give you three equations and three unknowns. Then you will be able to solve those equations for T1, T2 and a.

AM
 

1. What is an Atwood Machine?

An Atwood Machine is a device used to study the principles of acceleration and motion. It consists of a pulley, two masses (m1 and m2), and a string connecting the masses over the pulley.

2. What is the acceleration of m1 in an Atwood Machine?

The acceleration of m1 in an Atwood Machine is equal to the net force acting on m1 divided by its mass (a = F/m1). This can be calculated using the equation a = (m2 - m1)g / (m1 + m2), where g is the acceleration due to gravity.

3. How does the acceleration of m1 change with different masses?

The acceleration of m1 in an Atwood Machine is directly proportional to the difference in masses between m1 and m2. As the difference in masses increases, the acceleration of m1 also increases. However, the acceleration is inversely proportional to the total mass of the system. As the total mass increases, the acceleration decreases.

4. What factors affect the acceleration of m1 in an Atwood Machine?

The acceleration of m1 is affected by the difference in masses between m1 and m2, as well as the total mass of the system. It is also affected by the force of gravity and any external forces acting on the masses. Friction and air resistance can also affect the acceleration.

5. How is the acceleration of m1 related to the tension in the string?

The acceleration of m1 is directly proportional to the tension in the string. As the acceleration increases, so does the tension in the string. This is due to Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = ma). In this case, the tension in the string is the net force acting on m1, causing it to accelerate.

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