Two radii pulley lifting a pack

• getty102
Also, check your use of units as it might be causing errors.In summary, the question involves a pulley with a moment of inertia of 676 kgm2, a tension of 477.9 N, and a pack with a mass of 30.8 kg attached to the inner radius. Using the equations Ʃtorque=(I)(α) and ƩF=ma, the linear acceleration of the pack can be found by solving for the tension due to the pack on the pulley and summing the torques. The resulting expression is at=[R(Tyr)-r(mp*g)]/[(I/R)-(r*mp)], which should be checked for accuracy in terms of direction and units.
getty102

Homework Statement

You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I=676 kgm2 as shown. The tension in the rope that you are pulling is 477.9 N. A pack of mass 30.8 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.56 m and the outer radius is 0.8 m, what is the magnitude of the linear acceleration of the pack?

Homework Equations

Ʃtorque=(I)($\alpha$)
ƩF=ma

The Attempt at a Solution

I found the tension due to the mass of the pack on the pulley.
Tps=mp(g-at)
p=pack, at=linear acceleration of pack

I then summed the torques, and inserted the tension due to the pack on the pulley
R(Tyr)-r(mp(g-at))=I(at/R)

solved for at=[R(Tyr)-r(mp*g)]/[(I/R)-(r*mp)]

my final at=24.233 m/s/s which is not right

You might want to check your expression for Tps. Make sure that the implied forces result in an acceleration in the desired direction for the pack.

What is a two radii pulley lifting a pack?

A two radii pulley lifting a pack refers to a system where two pulleys are connected by a rope or belt, with one pulley attached to a fixed point and the other attached to a load. The pulleys have a radius that determines the mechanical advantage of the system, allowing for easier lifting of heavy objects.

How does a two radii pulley lifting a pack work?

The two radii pulley lifting a pack works by distributing the weight of the load between the two pulleys. As one pulley is pulled down, the other pulley is pulled up, and the load is lifted with less force needed from the person pulling the rope or belt. The larger the radius of the pulleys, the greater the mechanical advantage and the easier it is to lift the load.

What are the advantages of using a two radii pulley lifting a pack?

The main advantage of using a two radii pulley lifting a pack is the mechanical advantage it provides. By using a system of pulleys, the load can be lifted with less force, making it easier for a person to lift heavy objects. This can be particularly useful in situations where there is limited strength or space available.

What factors affect the efficiency of a two radii pulley lifting a pack?

The efficiency of a two radii pulley lifting a pack can be affected by several factors, including the weight of the load, the friction of the pulleys, and the angle at which the rope or belt is pulled. The number and size of the pulleys also play a role in the efficiency of the system.

Are there any safety considerations when using a two radii pulley lifting a pack?

Yes, there are some safety considerations to keep in mind when using a two radii pulley lifting a pack. It is important to make sure that the pulleys and rope or belt are in good condition and can handle the weight of the load. Proper lifting techniques should also be used to avoid strain or injury. Additionally, it is important to secure the load and ensure that it does not shift or fall during lifting.

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