# Calculating the Fourth Mass: A Rope and Four Masses

• Dekoy
In summary, the problem involves four masses hanging from a ceiling with two tensions and three masses already measured. The goal is to find the fourth mass, which can be expressed as m4 =[m1T2/(T1 − T2)]− m2 − m3 using the equations F=ma, F1=-F2, and T=ma. The solution involves solving for g and substituting it into the equations to solve for m4. The figure accompanying the problem was not provided, but the problem was figured out independently.
Dekoy

## Homework Statement

2. There are four masses hanging by a rope from the
ceiling, as shown in the figure. Two of the tensions
and three of the masses have been measured.
Show that the fourth mass can be expressed as
m4 =[m1T2/(T1 − T2)]− m2 − m3.

## Homework Equations

F=ma, F1=-F2, T=ma

## The Attempt at a Solution

I think that (m1+m2+m3+m4)g=T1 and (m2+m3+m4)g=T2
I tried solving for g and substituting and try and solve for m4 but I just find it impssible to do.

We can't help you unless we see the figure that goes with this question.

I tried copying and pasting from a pdf file but it didn't work but it's really easy actually I already figured it out, :). Thanks anyways.

## 1. How do you calculate the fourth mass in a system with a rope and four masses?

To calculate the fourth mass in this system, you will need to use the equation: M4 = (M1 + M2 + M3) / 3. This equation takes into account the masses of the three known objects and divides by three to find the fourth mass.

## 2. What units should be used when calculating the fourth mass in this system?

The units used for the masses should be consistent, whether it is kilograms, grams, or any other unit of mass. The resulting fourth mass will have the same units as the input masses.

## 3. Can the fourth mass be negative?

No, the fourth mass cannot be negative. The equation used to calculate the fourth mass assumes that all masses are positive. If the calculated fourth mass is negative, it is likely due to an error in the input masses.

## 4. How accurate is the calculated fourth mass?

The accuracy of the calculated fourth mass depends on the accuracy of the input masses. If the input masses are measured accurately, then the calculated fourth mass will also be accurate. However, there may be slight variations due to experimental error.

## 5. What other factors should be considered when calculating the fourth mass in this system?

Apart from the masses of the objects, other factors that may affect the fourth mass include the length and tension of the rope, as well as any external forces acting on the system. These factors may need to be taken into account for more precise calculations.

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