Deriving a formula for atwoods Machine

In summary, in this conversation, the topic is Atwood's machine, which consists of two containers connected by a cord over a frictionless pulley. At time t = 0, the first container has mass m1 and the second container has mass m2, with m1 < m2. The first container is losing mass at a constant rate r. The questions asked are: (a) What is the rate of change of acceleration at time t? (b) When will the second container reach maximum acceleration? The answer to (a) is that the rate of acceleration is equal to the rate of mass change, r, divided by the total mass, (m2 + m1). The answer to (b) is not
  • #1
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Homework Statement


Figure 5-53 shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0 container 1 has m1 and container 2 has mass m2 with m1 < m2, but container 1 is losing mass (through a leak) at the constant rate r. (a) At what rate is the magnitude of acceleration of the containers changing at time t? (b) When will container 2 reach maximum acceleration? Express your answers in terms of the variables given and g.

Just having trouble with this question, not sure where to go after obtaining

a = (m2 - m1)g/(m2 + m1)
 
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  • #2
Homework Equations Newton's 2nd law, F = maThe Attempt at a Solution From what I can see, the acceleration is changing at the rate that the two masses are changing. So the rate of acceleration would be equal to the rate of the mass change, r, divided by the total mass, (m2 + m1)? I'm really not sure how to approach this problem though.
 

What is an Atwood's Machine?

An Atwood's Machine is a simple mechanical device consisting of two masses connected by a string or cable that passes over a pulley. It is commonly used in physics experiments to study and demonstrate concepts of force, acceleration, and tension.

Why is it important to derive a formula for Atwood's Machine?

Deriving a formula for Atwood's Machine allows us to predict the relationship between the two masses and the acceleration of the system. This can help us understand and apply principles of physics in real-world scenarios.

What variables are involved in the formula for Atwood's Machine?

The formula for Atwood's Machine involves the masses of the two objects (m1 and m2), the acceleration of the system (a), and the gravitational force (g).

How is the formula for Atwood's Machine derived?

The formula for Atwood's Machine is derived using principles of Newton's laws of motion and the concept of tension in a string or cable. By analyzing the forces acting on the two masses, we can arrive at the formula a = (m1 - m2)g / (m1 + m2).

What are some practical applications of the formula for Atwood's Machine?

The formula for Atwood's Machine can be applied in various scenarios, such as determining the optimal weight distribution for elevators, calculating the tension in cables of cranes and other lifting equipment, and understanding the mechanics of pulley systems in engineering and construction.

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