How Do You Solve a Frictionless Pulley System Problem?

AI Thread Summary
The discussion revolves around solving a frictionless pulley system problem involving a 4.00 kg block on a horizontal surface and a hanging block with unknown mass m. The tension in the rope is given as 10.0 N, and participants are trying to determine the acceleration of the blocks and the mass m. One user initially calculated the mass m as 0.813 kg but was informed that the correct answer is 1.37 kg. The conversation emphasizes the importance of consistent direction in free body diagrams and understanding the acceleration of both blocks in the system. Accurate analysis of forces and directions is crucial for solving such physics problems effectively.
Yosty22
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Homework Statement



A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 10.0N.
a.What is the acceleration of either block?
c.Find the mass m of the hanging block.

Homework Equations



ƩF=ma

The Attempt at a Solution



My attempt at solving the problem is attached. Can someone tell me where I went wrong?
(It got cut off at the bottom, it just says that my answer of 0.813kg is wrong, but I don't know why. THE CORRECT ANSWER IS: m=1.37kg
 
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Sorry, My attempt at the solution is now attached.
 

Attachments

You've been inconsistent in your choice of directions. Which way is the mass m accelerating?
 
Recheck your free body diagram. Where are the blocks accelerating? Specifically, on what axis as I am seeing two different axis here and that is not correct.

EDIT: Sorry, didn't see haruspex's post when I responded, I did the same problem.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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