Two blocks with different mass are attached to either end of a light rope that passes

In summary, the problem involves two blocks with different masses attached to a light rope over a light, frictionless pulley. One block starts to descend from rest and after traveling 1.30 m, its speed is measured to be 3.50 m/s. With a total mass of 14.0 kg, the more massive block's mass can be found by using the equations v^2 = u^2 + 2as and F = ma. By setting up and solving simultaneous equations, the mass of the more massive block can be determined.
  • #1
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Homework Statement


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 1.30 m, its speed is 3.50m/s .

If the total mass of the two blocks is 14.0 kg, what is the mass of the more massive block?



Homework Equations



(1/2)mv1^2+mgy1=(1/2)mv2^2+mgy2

The Attempt at a Solution


Can someone help me get started with this problem? I'm not sure I am using the right equation or approaching it correctly
 
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  • #2
Since you know that a 14 Kg mass has been accelerated from rest to 3.50 m/s over a distance of 1.30 m, you can detemine the acceleration from the equation:
[tex]v^{2} = u^{2} + 2as[/tex]

From there you can calculate the force required to accelerate the mass at that rate with:
[tex]F = ma[/tex]

That will give you the difference in the weights of the two masses.
 
  • #3
What does u^2 stand for?
 
  • #4
v is the final velocity, u is the initial velocity. Perhaps you use a different type of notation. The same formula is listed last here in a different notation.
 
  • #5
I found that the F=ma is 65.94N, but where do I go from there?
 
  • #6
Like I said, that's the difference in their weights (though I actually get 65.96 N). You can divide that by g to find the difference in their mass since weight = mass * gravitational field strength.

If you call the two weights a and b, that will give you:
a - b = 65.96/g

You also have
a + b = 14

Now you have to solve the simultaneous equations.
 
  • #7
Thanks, I got it. You guys are amazing
 
  • #8
Nah, not amazing just ... yeah OK, amazing. :wink:

Happy to help. :smile:
 
  • #9


This appears to be a common question. I got the same thing with different values, but the formulae here worked!
 

1. How does the mass of the blocks affect the tension in the rope?

The tension in the rope is directly proportional to the mass of the blocks. This means that as the mass of the blocks increases, so does the tension in the rope. This is because the rope needs to support the weight of both blocks.

2. What happens to the tension if one block is heavier than the other?

The tension in the rope will be greater on the side with the heavier block. This is because the heavier block will pull down with a greater force, causing the rope to stretch and increase the tension.

3. Is there a limit to the tension that the rope can handle?

Yes, there is a limit to the tension that the rope can handle. Every rope has a breaking point, and if the tension exceeds this point, the rope will break. The breaking point of a rope depends on its material and thickness.

4. What happens to the tension if the blocks are moved closer together?

If the blocks are moved closer together, the tension in the rope will increase. This is because the distance between the blocks decreases, which means that the rope has to support the weight of the blocks over a shorter distance, resulting in a higher tension.

5. How does the length of the rope affect the tension?

The longer the rope, the lower the tension will be. This is because the weight of the blocks is spread out over a longer distance, reducing the force on the rope and decreasing the tension. Similarly, a shorter rope will have a higher tension as the weight of the blocks is concentrated over a shorter distance.

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