Conservation of Energy within a pulley system

In summary, two objects connected by a light string are released from rest, with the 5.87 kg object starting at a height of 2.55m above the floor. The acceleration of gravity is 9.8 m/s^2. We need to calculate the speed of both objects right before the 5.87 kg object hits the floor, and the height that the 3.24 kg object travels after the 5.87 kg object hits the floor. To do this, we need to take into account the potential energy and kinetic energy of both objects as they are not a closed system. Conservation of energy (PE + KE = constant) only applies to a closed system.
  • #1
miamirulz29
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Homework Statement


Two objects are connected by a light string passing over a light frictionless pulley as shown in the figure. the 5.87 kg object is released from rest at a point 2.55m above the floor. The acceleration of gravity is 9.8 m/s^2. What is the speed of each object at the instant before the 5.87 kg object hits the floor. How much higher does the 3.24 kg object travel after the 5.87 kg object hits the floor.

Homework Equations


Ei = Ef

The Attempt at a Solution



The speed of the both objects are the same when both objects are moving. Because that is the case, I thought the answer would be v = sqrt(2gh), where h = 2.55m. However, that is not the case. Do I need to take into account the PE and KE of of the 3.24 kg object too?
 
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  • #2
hi miamirulz29! :smile:
miamirulz29 said:
Do I need to take into account the PE and KE of of the 3.24 kg object too?

yup! :biggrin:

one mass on its own is not a closed system

conservation of energy (PE + KE = constant) only works for a closed system :wink:
 

1. What is the conservation of energy within a pulley system?

The conservation of energy states that energy cannot be created or destroyed, but it can be transferred or transformed from one form to another. In a pulley system, the total amount of energy remains constant, but it can be distributed among the different parts of the system.

2. How does a pulley system conserve energy?

A pulley system conserves energy by efficiently transferring the input energy to the output energy. The input energy, such as human force or a motor's power, is used to lift or move an object. The potential energy gained by the object is then converted to kinetic energy as it moves, which can be used to perform work.

3. Are there any energy losses in a pulley system?

Although a pulley system is designed to conserve energy, there are still some energy losses due to friction. Friction between the pulley and the rope, as well as between different parts of the system, can result in a small amount of energy being converted to heat. However, these losses can be minimized by using lubricants and high-quality materials.

4. How can the efficiency of a pulley system be improved?

The efficiency of a pulley system can be improved by reducing the amount of friction and minimizing the weight of the moving parts. Using smooth and well-lubricated pulleys, as well as lightweight ropes or chains, can help to increase the efficiency of the system. Additionally, proper maintenance and regular inspections can also improve the overall efficiency.

5. Can a pulley system violate the law of conservation of energy?

No, a pulley system cannot violate the law of conservation of energy. The total amount of energy within a closed system, such as a pulley system, cannot change. If it appears that the output energy is greater than the input energy, it is likely due to human error in measurement or not accounting for all forms of energy, such as heat or sound.

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