2 Block and a pulley(has mass) system

In summary, the question is about why a block falls faster than the original when a single string is connecting two masses. The conversation discusses the use of Newton's second law and the free body diagram to find the expression for acceleration, which is independent of the radius of the pulley but dependent on the mass. Decreasing the mass of the pulley increases the acceleration.
  • #1
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Homework Statement



http://i43.tinypic.com/352nlw2.jpg

I need help with the question 25. The three star (hardest) problem.

Homework Equations


well conservation of energy is
Mgh=.5Mv^2+.5Mv^2+.5(.5MR^2) ω^2


The Attempt at a Solution


Wouldn't increasing the Radius increase the Inertia by a factor of 4 and decreasing the mass reduce it only by a factor of 2. So the velocity should be less due to the increased inertia and the block would fall slower.

Anyone have any idea why the block would fall faster than the original?
 
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  • #2
Since the single string is connecting the two masses, the acceleration of masses anfd the pulley must be the same. Let T1 be the tension in the horizontal segment of the string and T2 be the tension is the vertical segment of the string. Now draw the free body diagram. Applying Newton's second law, you have
T1 = ma ...(1)
Net torque τ = (T2 - T1)*R = I*α = 1/2*M*R^2*α. R*α = a. So
T2 - T1 = 1/2*M*a...(2)
mg - T2 = ma...(3)
From these equations find the expression for the acceleration a.
You can see that acceleration is independent of the radius of the pulley and it depends on the mass of the pulley.
In the acceleration expression the mass of the pulley appears in the denominator. So as mass decreases the acceleration increases.
 

What is a 2 block and a pulley system?

A 2 block and a pulley system is a simple machine that consists of two blocks or objects connected by a rope or cable that is looped around a pulley. The pulley is a wheel with a grooved rim that rotates on an axle and changes the direction of the force applied to the rope.

How does a 2 block and a pulley system work?

In a 2 block and a pulley system, one end of the rope is attached to a fixed point, while the other end is pulled by a force or weight. As the rope passes over the pulley, the direction of the force is changed, making it easier to lift the weight. This system reduces the amount of force needed to lift the weight, but the distance the rope must be pulled is increased.

What are the advantages of using a 2 block and a pulley system?

One of the main advantages of a 2 block and a pulley system is that it can decrease the amount of force needed to lift a heavy object. This makes it an efficient and useful tool in a variety of applications, such as construction, transportation, and manufacturing. It also allows for the weight to be lifted in a controlled and precise manner.

What are the different types of 2 block and a pulley systems?

There are two main types of 2 block and a pulley systems: fixed and movable. In a fixed system, one end of the rope is attached to a fixed point, while the other end is attached to the object being lifted. In a movable system, both ends of the rope are attached to the object being lifted, allowing for the weight to be moved horizontally as well as vertically.

What are some real-life examples of 2 block and a pulley systems?

Some common examples of 2 block and a pulley systems include elevators, cranes, flagpoles, and window blinds. These systems can also be found in everyday objects, such as exercise equipment, garage doors, and sailboat rigging. In addition, many industrial machines and processes use 2 block and a pulley systems to lift and move heavy objects.

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