# Mass Pulley System, Acceleration

• ryankunzzz
In summary, the problem involves a 1kg block on a 20° incline with a coefficient of friction μk=0.45, connected by a massless string to a frictionless pulley with a mass of 0.10kg and a hanging block of 2kg. The acceleration of the system is being calculated, taking into account rotational inertia. The relevant equations are Newton's 2nd law, ΣF=ma, ΣF=Iα for rotational motion, and ƒk=μN for friction. After drawing the free body diagrams, the equations for tension were used, but the radius of the pulley is still needed. After making corrections to the equations, the problem was successfully
ryankunzzz

## Homework Statement

A block of 1kg is resting on an incline of 20° that has a coefficient of friction μk=0.45 with the surface. It is connected with a mass less string to a friction-less pulley of mass 0.10 kg to a hanging block of 2 kg. What is the acceleration of the system without ignoring rotational inertia. Model the pulley as a disk.

## Homework Equations

First we need Newtons 2nd law, ΣF=ma
Also for rotational motion ΣF=Iα
and friction is ƒk=μN where N is the normal force.

## The Attempt at a Solution

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After drawing my free body diagrams, I was left with this :

But I'm stumped there, I feel like I'm missing something obvious.

I want to plug the two equations for the tensions into the pulley equation, but then I'm still missing the radius of the pulley.

EDIT: The -m2g in the last equation on the right should be m2a

EDIT #2: I forgot the R on the (T2-T1)=IAlpha, I solved it. Thanks.

Last edited:
Well done ... and good work doing all the algebra before subbing in the values.

## 1. What is a mass pulley system?

A mass pulley system is a mechanical system that consists of a mass attached to a pulley or series of pulleys, which are used to change the direction and magnitude of a force applied to the system. This system is often used to lift or move heavy objects with less effort.

## 2. How does a mass pulley system affect acceleration?

A mass pulley system can affect acceleration in several ways. First, the number and arrangement of pulleys can determine the mechanical advantage of the system, which affects the amount of force needed to move the mass and therefore the acceleration. Additionally, the mass of the pulley itself can add to the total mass of the system and affect the acceleration. Friction between the pulley and the rope or other components can also impact the acceleration of the system.

## 3. What factors influence the acceleration of a mass pulley system?

There are several factors that can influence the acceleration of a mass pulley system. These include the mass of the object being moved, the mass of the pulley and any other components in the system, the angle of the rope or cable, and any external forces such as friction or air resistance.

## 4. How do you calculate the acceleration of a mass pulley system?

The acceleration of a mass pulley system can be calculated using Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation for this is a = F/m, where a is the acceleration, F is the net force, and m is the mass of the object.

## 5. What are some real-world applications of mass pulley systems?

Mass pulley systems have numerous real-world applications, including elevators, cranes, and conveyor belts. They are also commonly used in weightlifting machines, sailboats, and even in some types of engines. Mass pulley systems are also utilized in physics experiments and demonstrations to study the effects of forces and acceleration.

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