# Calculating Speed of Descending Block B using Energy Methods

• ~angel~
In summary, the conversation discusses a system consisting of two blocks attached by a string, with one block resting on a table and the other hanging vertically from a pulley. The pulley has radius R and moment of inertia I, and the system is released from rest. The coefficient of kinetic friction between the table and the block is mu_k. The conversation focuses on using energy methods to calculate the speed of the hanging block as it descends, taking into account the rotational motion of the pulley. The final answer is obtained by equating the initial and final energies, which include kinetic and potential energies, as well as work done by friction.
~angel~
Ok...I don't have a picture for this but imagine a block A resting on a table. It is attached to a string which in turn is attached to a pulley on the edge of the table. This same string is attached to another block B, which is vertically hanging off the pulley.

The pulley has radius R and moment of inertia I. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between the table top and block A is mu_k. The system is released from rest, and block B descends. Block A has mass m_A and block B has mass m_B. Use energy methods to calculate the speed of block B as a function of the distance that it had descended.

I'm not sure how to incorporate hte moment of inertia and the rotational motion of the pulley.

Thank you.

~angel~ said:
I'm not sure how to incorporate hte moment of inertia and the rotational motion of the pulley.

The rotational energy of an object with moment of inertia, I, is just:

$$E=\frac{1}{2}I\omega^2$$

What are the other energies in the problem? What are their initial and final states?

Initial KE is zero. I'm not sure about PE. Say that we define the zero point to be the distance d block B has descended. Then it'll have PE m_B+g+d initially. Ihave no idea about the PE for block A, but coiuld it remain the same?

Final KE include (m_A*v_A^2)/2, (m_B*v_B^2)/2 and I*w^2/2. There is also friction...The work done by that is mu_k*m*g*d. Final PE is zero.

I'm not sure though.

That all looks right, assuming you meant the initial PE was m_B*g*d. Now just set them equal and solve.

Yeah, i meant that. So what exactly is the PE of block A...would that be m_A*g*d and remain the same during each state?

p.e of block A will remain same except for the fact if you want it to get off the surface on which it is resting

Ive got the answer. Thank you.

## What is the formula for calculating the speed of a descending block using energy methods?

The formula for calculating the speed of a descending block is v = √(2gh), where v is the speed in meters per second, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the block in meters.

## How do energy methods differ from other methods of calculating speed?

Energy methods involve using the principle of conservation of energy to calculate the speed of an object, while other methods such as using Newton's laws of motion involve considering external forces acting on the object.

## What are the steps involved in using energy methods to calculate speed?

The first step is to determine the initial potential energy of the object at its starting point. Then, calculate the final potential energy at its ending point. Next, equate these two energies and solve for the final velocity using the formula v = √(2gh).

## Are there any assumptions or limitations when using energy methods to calculate speed?

One assumption is that there are no external forces acting on the object during its descent, such as friction or air resistance. This method also assumes that all of the initial potential energy is converted into kinetic energy at the end.

## How can energy methods be applied to real-life scenarios involving descending objects?

Energy methods can be used to calculate the speed of objects such as falling rocks, roller coasters, or skydivers. This can help in determining the safety and efficiency of these objects in real-life situations.

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