Finding the masses of two blocks in a pulley system using work-energy theorem

In summary, the conversation discusses a scenario where two blocks with different masses are attached to a rope over a pulley. The more massive block starts to descend and after reaching a height of 1m, it has a speed of 1.50m/s. The total mass of the blocks is 13kg, and the conversation then tries to determine the individual masses of the blocks using the conservation of energy principle. However, there is some confusion about the formula used and it is suggested to start from the initial potential and kinetic energy of the system.
  • #1
ph123
41
0
Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.00m , its speed is 1.50m/s . If the total mass of the two blocks is 13kg, then what is:
1)the mass of the more massive block
2)the mass of the less massive block

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Since the more massive block descended 1m, then the less massive block must have ascended 1.0m. Also, since the more massive block travels at 1.50m/s, then the less massive block must trave -1.50m/s. Setting the height of the less massive block, m1, as 2.0m, and the height of the more massive block, m2, as 0, then

m1gh + (1/2)m1v1^2 = (1/2)m2v2^2
m1(gh + (1/2)v1^2) = m2(1/2 *v2^2)
m1/m2 = v2^2/(gh + v1^2)
m1/m2 = (1.125 m^2/s^2) / (20.725 m^2/s^2)
m1/m2 = 0.0543

I figured, since given only the combined mass, I had to find the ratio of the masses. I multiplied the ratio (0.0543) times 13kg, and found that m1 = 0.706kg, and 13kg - 0.706kg = 12.294kg. Not right, though. Anyone know where I went wrong?
 
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  • #2
Yeah. Your equation for conservation of energy isn't right. You didnt factor in the loss of gravitational potential energy of the heavier mass. It should be:

[tex]m_1gh+0.5m_1v_1^2=m_2gh+0.5m_2v_2^2[/tex]

That should help you out.
 
  • #3
But, since the height of m2 is set to zero, m2gh drops out. So then I'm left with my original formula, right?
 
Last edited:
  • #4
ph123 said:
But, since the height of m2 is set to zero, m2gh drops out. So then I'm left with my original formula, right?
You are setting the final mechanical energy of m1 equal to the final mechanical energy of m2. This is not a correct application of the law of conservation of energy, which states that, in the absence of non-conservative forces doing work, that the initial mechanical energy of the system is equal to the final mechanical energy of the system. I would start by taking the initial potential and kinetic energy of the system to be zero prior to the release of the blocks, at h=0, and go from there.
 

1. How do you determine the masses of two blocks in a pulley system using the work-energy theorem?

To find the masses of the two blocks in a pulley system using the work-energy theorem, you will need to measure the distance the blocks move, the force applied to the blocks, and the velocity of the blocks. From this information, you can use the work-energy theorem equation to solve for the masses.

2. What is the work-energy theorem and why is it useful in determining the masses of two blocks in a pulley system?

The work-energy theorem is a physics principle that states that the work done on an object is equal to the change in the object's kinetic energy. In the context of determining the masses of two blocks in a pulley system, this theorem allows us to relate the work done by the force applied to the blocks to the resulting change in their velocities, and ultimately the masses of the blocks.

3. Can the work-energy theorem be applied to any type of pulley system?

Yes, the work-energy theorem can be applied to any type of pulley system, as long as the necessary measurements and information are available. This theorem is a fundamental principle in physics and can be used to analyze the motion of objects in various systems.

4. Are there any assumptions or limitations when using the work-energy theorem to determine the masses of two blocks in a pulley system?

One of the main assumptions when using the work-energy theorem is that there is no energy lost due to friction or other external factors. This means that the work done by the applied force is equal to the change in kinetic energy of the blocks. Additionally, the work-energy theorem only applies to systems where the net force is constant and in the same direction as the displacement of the objects.

5. What are some practical applications of using the work-energy theorem to determine the masses of two blocks in a pulley system?

The work-energy theorem has many practical applications in real-world scenarios. For example, it can be used in engineering to determine the appropriate masses for counterweights in elevators or cranes. It can also be applied in sports, such as calculating the mass of a shot put or javelin based on the distance it is thrown, or in determining the weight of a sled based on the energy required to pull it a certain distance. Additionally, the work-energy theorem plays a crucial role in understanding the motion of objects in roller coasters and other amusement park rides.

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