# Atwood System - max. height of the lighter object

• laurs
In summary: If an object is launched vertically with some initial speed, how high above the launch point will it get before it begins descending?In summary, the lighter object reaches a maximum height of 4.83 m after the system is released.
laurs
Homework Statement
The two masses are each initially 2.60 m above the ground, and the massless frictionless pulley is 10.00 m above the ground. The masses are m1 = 1.71 kg and m2 = 4.59 kg. What maximum height does the lighter object reach after the system is released?
(Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground.
This is its "launch" speed. Assume it doesn't hit the pulley.)
Relevant Equations
a = (m2-m1)(g)/(m2+m1)
vf^2 = vi^2 + 2ad
Fnet = ma
Fg = mg
Magnitude of acceleration of system:
a = (4.59kg - 1.71kg)(9.81N/kg)/(4.59kg + 1.71kg)
= 4.48 m/s^2

Velocity of lighter mass when heavier one hits the ground:
vf^2 = vi^2 + 2ad
= 0 + 2(4.48m/s^2)(2.60m)
vf = 4.83 m/s [up]

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?

laurs said:
Homework Statement: The two masses are each initially 2.60 m above the ground, and the massless frictionless pulley is 10.00 m above the ground. The masses are m1 = 1.71 kg and m2 = 4.59 kg. What maximum height does the lighter object reach after the system is released?
(Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground.
This is its "launch" speed. Assume it doesn't hit the pulley.)
Homework Equations: a = (m2-m1)(g)/(m2+m1)
vf^2 = vi^2 + 2ad
Fnet = ma
Fg = mg

Magnitude of acceleration of system:
a = (4.59kg - 1.71kg)(9.81N/kg)/(4.59kg + 1.71kg)
= 4.48 m/s^2

Velocity of lighter mass when heavier one hits the ground:
vf^2 = vi^2 + 2ad
= 0 + 2(4.48m/s^2)(2.60m)
vf = 4.83 m/s [up]

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?
laurs said:
I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?
Hello, @laurs .

It's helpful to include all information in the body of your post, even if it's also included in thread's title.

Many of us are familiar with Atwood's machine. (Atwood system as you refer to it.) However, the point at which you are puzzled, indicates that you may not be familiar with it.

Is this the case?

Hi @SammyS
I am familiar with the machine, however am not accustomed to seeing questions asking for the height of the lighter weight. Most of the questions ask about the acceleration or the forces acting on the weights, which is a simple calculation, but I don't really know how to approach this one. I have been able to calculate time as well, assuming initial speed is 0, using the vf = vi + at, getting a value of t = 1.077s, but still am unsure how to approach the projectile portion of the question.

laurs said:
Hi @SammyS
I am familiar with the machine, however am not accustomed to seeing questions asking for the height of the lighter weight. Most of the questions ask about the acceleration or the forces acting on the weights, which is a simple calculation, but I don't really know how to approach this one. I have been able to calculate time as well, assuming initial speed is 0, using the vf = vi + at, getting a value of t = 1.077s, but still am unsure how to approach the projectile portion of the question.
As for the point you're stuck on:
laurs said:
...

I am not sure what to do from here? I don't really understand what the hint means by launch speed, like is the mass flying out of the pulley into a parabolic trajectory?
The direction of "launch" is vertically upward at a distance of 5.20 m above the ground. The pulley is not involved. It's 10.00 m above the ground.

If an object is launched vertically with some initial speed, how high above the launch point will it get before it begins descending?

## 1. What is an Atwood System?

An Atwood System is a simple mechanical system consisting of two objects connected by a string or rope that passes over a pulley. The objects are typically different in mass and are subject to gravitational forces. This system is often used to demonstrate principles of physics, such as Newton's second law of motion.

## 2. How does the Atwood System work?

In an Atwood System, the heavier object will exert a greater gravitational force on the string, causing it to accelerate downward. As a result, the lighter object will accelerate upward at the same rate. This creates a continuous motion between the two objects as they exchange positions.

## 3. What is the maximum height that the lighter object can reach in an Atwood System?

The maximum height that the lighter object can reach in an Atwood System is equal to half the length of the string connecting the two objects. This is because at this point, the potential energy of the lighter object is at its maximum and is equal to the potential energy of the heavier object.

## 4. How is the maximum height of the lighter object affected by the masses of the objects?

The maximum height of the lighter object is directly proportional to the difference in mass between the two objects. As the mass of the heavier object increases, the maximum height of the lighter object also increases.

## 5. What factors can affect the maximum height of the lighter object in an Atwood System?

The maximum height of the lighter object can be affected by factors such as the mass and weight of the objects, the length and tension of the string, and the presence of external forces such as friction. It can also be affected by the acceleration due to gravity, which varies depending on the location on Earth.

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