# Find all the accelerations of the 3 masses and the 1kg pulley

• paul_harris77
In summary, The conversation discusses a question about tension in a mass system with pulleys and finding accelerations and tensions in the ropes. The question also raises a confusion about simplifying the system to just two masses. The expert explains that the individual masses on the right hand side are accelerating at different rates, so they cannot be replaced with a single mass with one acceleration.
paul_harris77
Dear All

I have a question about tension in a mass system with pulleys.

The question asks you to find all the accelerations of the 3 masses and the 1kg pulley. It also asks you to find the tensions in the ropes.

I have used d'Alembert's principle to do this and appear to have the correct answer for the tensions of 33N for the big pulley rope and 12N for the 1kg pulley rope (assuming g=10ms-2)

After doing this though, I am slightly confused. Surely the system could be simplified to the 3 kg mass on the left of the big pulley and a 4kg mass on the right hand side (eliminating the 1kg pulley). Then the tension in the remaining rope would be (4-3)g = 10N instead of 33N. Why is this not right?

Many thanks

Regards

Paul

They 4kg mass you replace necessarily accelerates at one rate while the individual masses on the RHS are accelerating at different rates. They are not exerting the same reaction forces as their static weights so they don't "just add up".

Consider a third example of a simple pulley with two masses and a third mass on the right being dropped. It isn't appropriate to add in this third mass right? But why not?

paul_harris77 said:
Surely the system could be simplified to the 3 kg mass on the left of the big pulley and a 4kg mass on the right hand side (eliminating the 1kg pulley).
You can't replace a system with internal parts that accelerate differently with a single mass with a single acceleration. (Note that the force exerted on the 1 kg pulley by the hanging masses does not simply equal the weight of the hanging masses.)

## What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

## How do you calculate acceleration?

Acceleration can be calculated by dividing the change in velocity by the change in time. This is represented by the equation a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## What are the units of acceleration?

The units of acceleration are meters per second squared (m/s²) in the metric system and feet per second squared (ft/s²) in the imperial system. Other units include kilometers per hour squared (km/h²) and miles per hour squared (mi/h²).

## How do you find the acceleration of an object on an incline?

To find the acceleration of an object on an incline, you can use the equation a = gsinθ, where a is acceleration, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline.

## What is the acceleration of the 1kg pulley in this scenario?

The acceleration of the 1kg pulley in this scenario can be calculated by using the equation a = (m1g - m2g) / (m1 + m2), where m1 and m2 are the masses on either side of the pulley and g is the acceleration due to gravity. This assumes that the pulley has negligible mass and does not contribute to the overall acceleration.

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