Calculate Acceleration & Tension of a Pulley System

[Ciaran]

Homework Statement

Three equal masses are hung from a pulley(2 on one side, 1 on the other). Find the acceleration of the system and the tension between: a) the 2 sides of the pulley and b) between the 2 masses on the same side

Homework Equations

The Attempt at a Solution

Got a= g/3, for a) T= 13.3m N and not 100% sure about b)

 

[Doc Al]

Got a= g/3, for a) T= 13.3m N

Good.

and not 100% sure about b)

What do you think? Apply Newton's 2nd law to one of those masses.

 

[Ciaran]

Is it T= 2g/3 N?

 

[Doc Al]

Is it T= 2g/3 N?

Yes, but you left out the mass.

(It's generally a good policy to show how you arrived at your answer, not just give your answer.)

 

[HalfLostAndSearching]

First, it is important to clarify the setup of the pulley system. From the given information, it seems that there are three masses hanging from the pulley, with two on one side and one on the other. It is also not clear whether the pulley is fixed or movable. For the purpose of this response, I will assume that the pulley is fixed.

To calculate the acceleration and tension in this system, we can use Newton's laws of motion. Let's label the two sides of the pulley as A and B, with the two masses on side A being m1 and m2, and the mass on side B being m3. We can also assume that the masses are equal, so m1 = m2 = m3 = m.

First, let's consider the forces acting on each mass. On side A, we have the weight of m1 and m2 pulling downwards, and the tension force from the rope pulling upwards. On side B, we have the weight of m3 pulling downwards and the tension force from the rope pulling upwards. Since the pulley is fixed, the rope must also be pulling on the pulley, creating a tension force on both sides.

Using Newton's second law, we can write the following equations for the forces on each mass:

For m1 and m2:
ΣF = ma
T - m1g = m1a
T - m2g = m2a

For m3:
ΣF = ma
T - m3g = m3a

We can also use the fact that the masses are equal, so m1 = m2 = m3 = m, to simplify these equations:

For m1 and m2:
T - mg = ma
T - mg = ma

For m3:
T - mg = ma

Next, we can solve for the acceleration by adding the equations for m1 and m2 and substituting in the value for T from the equation for m3:

2T - 2mg = 2ma
T - mg = ma
T = 3ma

Solving for a, we get:
a = T/3m

Since we know that T = 13.3 N, and m is the mass of each of the three masses, we can substitute those values in to get the acceleration of the system. However, it is important to note that the units for mass must be in kilograms,