Multiple Pullys and determing Tension

In summary, the conversation discusses the use of multiple pulleys and determining tension dynamics in a block-pulley system. The equations for the tension in each block-pulley system and on the ramp are given, but the question focuses on finding an equation to relate the three accelerations using conservation of string. The answer is identified as d, but the process to reach that answer is still unknown.
  • #1
e4canadian
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Multiple Pulleys and determing Tension Dynamics

So i started out with the the equation for the tension of the block-pulley system on the far left in the y direction being: 2T-2g = 2*a1
the equation for the middle block-pulley system is: 2T-2g = 3*a2
the equation for the block on the ramp is: T - 20*9.8*sin60 = 20a3

I need an equation to relate the three accelerations using conservation of string but i do not know how to write it.
 

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I am studying for a midterm and this is a question from a previous years midterm the answer is d, but i do not know how to get it.
 

1. How do multiple pulleys affect the tension in a system?

Multiple pulleys can either increase or decrease the tension in a system. If the pulleys are set up in a way that the load is shared over multiple strands of rope, the tension will decrease. However, if the pulleys are set up in a way that adds the tension from each strand of rope, the tension will increase.

2. How do you determine the tension in a system with multiple pulleys?

To determine the tension in a system with multiple pulleys, you first need to identify the direction of the applied force and the direction of the load. Then, draw a free body diagram and use the equations of motion to calculate the tension in each rope. Finally, add up all the tensions to determine the total tension in the system.

3. What is the mechanical advantage of using multiple pulleys?

The mechanical advantage of using multiple pulleys is the ratio of the output force to the input force. In a system with multiple pulleys, the mechanical advantage is equal to the number of strands supporting the load. This means that the more pulleys you have, the less force you need to apply to lift a heavy load.

4. How does the number of pulleys affect the efficiency of a system?

The number of pulleys in a system does not affect the efficiency, as long as the pulleys are well-maintained and there is no friction present. In an ideal system, the efficiency of a pulley system is always 100% as the work input is equal to the work output. However, in real-life scenarios, there may be some friction present, which can decrease the efficiency of the system.

5. Can multiple pulleys be used to lift an object heavier than the input force?

Yes, multiple pulleys can be used to lift an object that is heavier than the input force. This is possible because the mechanical advantage of a pulley system can be greater than 1. However, keep in mind that the more pulleys used, the longer the distance the rope needs to be pulled to lift the load, resulting in more work being done.

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