Sled pulled up incline at an angle with friction

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SUMMARY

The discussion centers on the physics problem involving a 3.6 kg sled being pulled at a 25-degree angle on a slope inclined at 15 degrees. The sled moves at a constant velocity with a tension of 16 N, leading to the calculation of friction and acceleration upon release. The user calculated the coefficient of friction (μ) as 0.131 and found the sled's acceleration to be 1.3 m/s² after release. However, the expected answer is 0.67 m/s², indicating a potential error in the calculations or assumptions made regarding forces acting on the sled.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Knowledge of friction and its coefficient (f=μN)
  • Ability to resolve forces into components (e.g., tension and gravitational force)
  • Familiarity with trigonometric functions (sine and cosine) in physics applications
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  • Review the concept of force resolution in inclined planes
  • Study the effects of tension and friction on motion
  • Learn about the relationship between constant velocity and net force
  • Explore common pitfalls in calculating acceleration in physics problems
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Students studying physics, particularly those focusing on mechanics and inclined planes, as well as educators looking for examples of force analysis in real-world applications.

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Homework Statement



A child pulls a 3.6 kg sled at 25 degrees to a slope that is 15 degrees to the horizontal, as in the figure. The sled moves at a constant velocity when the tension is 16 N. What is the acceleration of the sled if the rope is released?


Homework Equations



F=ma, f=\muN


The Attempt at a Solution



Constant velocity means that friction + the component from Fg shall equal FTx (tension component parallell to plane) that is FTx = f + Fx

Where FTx=cos(25)*FT=14.5 N and Fx=3.6*9.8=9.13 N

Now I want \mu so that I can calculate f. And we know that N=cos(15)*mg+T*sin(25)=40.84 N

If we go back to the start, FTx=\muN+Fx so \mu= \frac{ (F<sub>Tx</sub>-F<sub>x</sub>) }{N}= \frac{14.5-9.13}{40.84} = 0.131

When we release the sled N will reduce to N=mg*cos(15)=34.08 and so f=0.131*34.08=4.46 N

Fres=Fx-f=9.13-4.46=4.66 N

And the acceleration is a=\frac{F}{m}=\frac{4.66}{3.6}=1.3 m/s^2

But apparently this is not correct. Could someone please tell me what I've missed, this question has been very frustrating for me :(

Also, negative signs tend to mess upp my Latex, I apologize.
 
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Here's the figure btw.
 

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Anyone?
According to the answer sheet the correct answer should be 0.67 m/s^2 but I'm starting to wonder whether that's true or not?
 

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