What Is the Acceleration of a Block in a Pulley System?

In summary, a 24 kg block with a pulley attached slides along a frictionless surface and is connected by a massless string to a 5.3 kg block. The equations used to solve for the acceleration of the 24 kg block and the tension in the connecting string are 24a1 = 2T and 5.3g - T = 5.3a2. However, a third equation is needed to solve for the unknown variables due to the nature of the pulley system. The relationship between the accelerations of the two blocks can be used as the third equation to find the solutions.
  • #1
physicsnerd11
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Homework Statement



A 24 kg block with a pulley attached slides along a firctionless surface. It is connected by a massless string to a 5.3 kg block via the arrangement shown. a) Find the acceleration of the 24 kg block. b) Find the tension in the connecting string.

Homework Equations



F = ma

The Attempt at a Solution



For the 24 kg, I thought that 24a = 2T. Then 5.3g - T = 5.3a.
Then set the two equal to each other, so I got a = 3.005 m/s. However, that answer is incorrect. Part b, I would just plug in the part a answer, but my part a answer is incorrect. Please help with setup, etc. Thank you!
 
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  • #2
Hello physicsnerd11,

Welcome to Physics Forums!
physicsnerd11 said:

Homework Statement



A 24 kg block with a pulley attached slides along a firctionless surface. It is connected by a massless string to a 5.3 kg block via the arrangement shown. a) Find the acceleration of the 24 kg block. b) Find the tension in the connecting string.

Homework Equations



F = ma

The Attempt at a Solution



For the 24 kg, I thought that 24a = 2T. Then 5.3g - T = 5.3a.
Then set the two equal to each other, so I got a = 3.005 m/s. However, that answer is incorrect. Part b, I would just plug in the part a answer, but my part a answer is incorrect. Please help with setup, etc. Thank you!
It's difficult to give you help without a figure, diagram, or description of the system. I can only guess what the specific arrangement is.

But I'm guessing there is some sort of pulley system involved. If so, it means that the two blocks have different velocities, and different accelerations.

So change your equations to something like

24a1 = 2T
5.3g - T = 5.3a2

giving you 2 equations and 3 unknowns. You'll need a third equation to solve this. Given the simple nature of the pulley system, what is relationship between one block's acceleration compared to the other's? :wink:
 

FAQ: What Is the Acceleration of a Block in a Pulley System?

How do pulleys work in a block and tackle system?

In a block and tackle system, pulleys are used to change the direction of the force needed to lift an object. The more pulleys that are used, the less force is required to lift the object. This is because the weight of the object is distributed across multiple ropes and pulleys, making it easier to lift.

How do you calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is calculated by dividing the weight of the object being lifted by the force applied to the rope. For example, if a 100-pound object is being lifted with a force of 25 pounds, the mechanical advantage would be 4 (100/25 = 4).

What is the difference between fixed and movable pulleys?

A fixed pulley is attached to a stationary object and only changes the direction of the force. A movable pulley is attached to the object being lifted and moves with it, providing a mechanical advantage by distributing the weight of the object across multiple ropes and pulleys.

How does the number of pulleys affect the effort force needed to lift an object?

The more pulleys that are used in a block and tackle system, the less effort force is required to lift an object. This is because the weight of the object is distributed across multiple ropes and pulleys, reducing the amount of force needed to lift it.

Are there any disadvantages to using a pulley system?

One disadvantage of using a pulley system is that there is a trade-off between the mechanical advantage gained and the distance the rope needs to be pulled. In other words, the more pulleys that are used, the longer the rope needs to be pulled to lift the object. Additionally, pulleys can introduce friction, which can decrease the efficiency of the system.

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