# Two masses connected by a pulley with a frictionless table

• AHinkle
In summary, the conversation is about solving for the tension and acceleration in a system of two masses connected by a string. The equations for each mass's net force in the y and x directions are given, and the conversation ends with the correct solution for the acceleration and tension values based on the given masses and gravitational acceleration.
AHinkle

## Homework Equations

m1
$$\Sigma$$Fy=N-m1g = 0
$$\Sigma$$Fx=T=m1a
(Because there's no friction i see no opposing force to T)

m2
$$\Sigma$$Fy=m2g-T=m2a
$$\Sigma$$Fx=0

## The Attempt at a Solution

m2g-T=m2a
T=m1a

(m1+m2)a=m2g-T+T
I notice that the T's cancel when i add the equations together
so it becomes

(m1+m2)a=m2g
so...
a=(m2g)/(m1+m2)

so...
T=m1a
T=(m1) (m2g)/(m1+m2)

m1=6.03kg
m2=4.68kg

T=(6.03Kg)((4.68Kg)(9.8)/(6.03Kg+4.68Kg))
so...
T=25.8225N

T=m1a
25.8225N = (6.03Kg)a

a=4.2823 m/s2
did i do this right?

AHinkle said:
m2g-T=m2a
T=m1a

(m1+m2)a=m2g-T+T
I notice that the T's cancel when i add the equations together
so it becomes

(m1+m2)a=m2g
so...
a=(m2g)/(m1+m2)
You know, you could have just plugged the numbers in here and saved yourself some work.
a=4.2823 m/s2
'Looks right to me.

## 1. What is the purpose of the pulley in this system?

The pulley in this system is used to change the direction of the force being applied to the masses. It allows for one mass to move up while the other moves down, creating a balanced system.

## 2. How does the frictionless table affect the movement of the masses?

The frictionless table reduces the amount of friction present in the system, allowing for the masses to move more easily and without any extra resistance. This allows for a more accurate representation of the forces and movement in the system.

## 3. What is the role of gravity in this system?

Gravity is the force that is pulling the masses towards the ground. It creates a downward force on each mass, causing them to move in opposite directions when connected by the pulley.

## 4. How does the mass of each object affect the overall motion of the system?

The mass of each object affects the acceleration of the system. The heavier object will experience a greater force of gravity and therefore, accelerate at a slower rate than the lighter object. This difference in acceleration creates the movement of the masses towards each other.

## 5. What is the relationship between the tension in the string and the acceleration of the masses?

The tension in the string is equal to the force being applied to the masses. As one mass moves down, the other moves up, causing a change in tension. This change in tension creates an acceleration of the masses towards each other, with the magnitude of the acceleration being directly proportional to the difference in the masses and the tension in the string.

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