# How to Solve for missing mass in a Atwood's Machine?

• Not a Wrench
In summary, the conversation discusses a problem involving a gun being fired from a 200 meter cliff towards an Atwood's machine that is also suspended 200 meters in the air. The goal is to find the mass of the unknown object needed to make the bullet and a 20kg monkey meet at the same time. The solution involves finding the time at which the bullet will travel 200 meters, which is 4/15 seconds, and using this to solve for acceleration. However, the given numbers in the problem do not seem to make sense and the solution does not match up with standard equations. The accuracy of the problem is questioned and it is suggested to check for errors in the given information.
Not a Wrench

## Homework Statement

A gun is fired from a 200 meter cliff 200 meters away from an Atwood's Machine that is also suspended 200 meters in the air with a monkey of 20kg on the ground and a second unknown mass pulling the first mass up. Find the mass of the unknown needed for the bullet and the monkey to meet.

## Homework Equations

a/2 * t = h - deltaY
T= 2*9.8/m2+20

I have no clue what else. I basically wrote everything that pertains to an atwood's machine

## The Attempt at a Solution

I first found the time at which the bullet would travel the 200 meters, which is 4/15 seconds. I then tried to solve the acceleration. I get to a= 9.8(m2-20/m2+20). I don't know where to go from here. I have a T formula with m2 but the a I just got wouldn't help me plug into that. Help?

Hello. Did you state all of the information that was given? For example, do you know the direction that the bullet was fired? Does the Atwood's machine start from rest at the moment the bullet is fired?

TSny said:
Hello. Did you state all of the information that was given? For example, do you know the direction that the bullet was fired? Does the Atwood's machine start from rest at the moment the bullet is fired?
The gun is fired along horizontally along the x axis. The Atwood machine has a constant acceleration. I'm working of a drawing of a problem that was in class today. It has all the information needed to solve:http://imgur.com/y7D08C4
I have done everything possible for Atwood machines but I keep getting an acceleration in the 1000s m/s^2.

Not a Wrench said:
The gun is fired along horizontally along the x axis.
So where exactly will the bullet be after 4/15s?

haruspex said:
So where exactly will the bullet be after 4/15s?
It will hit the monkey at 199.65 meters vertically. So the monkey needs to travel 199.65 meters in 4/15 seconds. When I plug into the (a/2)4/15=199.65 I get an acceleration of 1118.05 m/s^2 which seems wrong. Then plugging into the a=g*(m2-m1/m2+m1) equation I get a mass of -20.3537 for the other box?! I have no clue what I am doing wrong here.

Not a Wrench said:
It will hit the monkey at 199.65 meters vertically. So the monkey needs to travel 199.65 meters in 4/15 seconds. When I plug into the (a/2)4/15=199.65 I get an acceleration of 1118.05 m/s^2 which seems wrong. Then plugging into the a=g*(m2-m1/m2+m1) equation I get a mass of -20.3537 for the other box?! I have no clue what I am doing wrong here.
Hmmm.. the numbers in the question don't make any sense. There is no way the monkey could be raised far enough in the time.
The 750m/s is rather fast, but not crazily so. (About 2 to 6 times common values.) You'd have to slow it to about 45m/s to make it feasible.
Alternatively, is the 200m range wrong? It would work if that should be at least 3400m.

Please check very carefully that you have related the problem correctly.

Write out the standard equation for s in terms of a & t and compare that to your numerical equation you used to get your a value.

## 1. What is Atwood's Machine?

Atwood's Machine is a simple mechanical device consisting of two masses connected by a string or pulley system. It is used to demonstrate the principles of classical mechanics and can be used to calculate the acceleration due to gravity.

## 2. How do I calculate the missing mass in an Atwood's Machine?

To calculate the missing mass in an Atwood's Machine, you need to use the equation m1/m2 = a2/a1, where m1 and m2 are the masses on either side of the pulley system and a1 and a2 are the corresponding accelerations. Rearrange the equation to solve for the missing mass.

## 3. What are the units for calculating the missing mass in an Atwood's Machine?

The units for calculating the missing mass in an Atwood's Machine will depend on the units used for mass and acceleration. It is important to ensure that all units are consistent and either in SI units or in imperial units.

## 4. How does the angle of the pulley affect the calculation of the missing mass?

The angle of the pulley does not affect the calculation of the missing mass in an Atwood's Machine. The equation m1/m2 = a2/a1 still applies regardless of the angle of the pulley.

## 5. Can I use Atwood's Machine to calculate the mass of an unknown object?

Yes, you can use Atwood's Machine to calculate the mass of an unknown object by using the equation m1/m2 = a2/a1. However, this method may not be accurate if the pulley system has friction or if the masses are not evenly distributed.

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