Finding a velocity of an object moving down an inclined plane help

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SUMMARY

The discussion focuses on calculating the velocity of a block sliding down an inclined plane with friction. The block has a mass of 1.137 kg and the inclined plane is 2.592 m long, set at an angle of 7.688 degrees. The lower half of the plane has a coefficient of kinetic friction (μk) of 0.375, while the upper half has a coefficient of kinetic friction (μk') of 0.087. The user initially misapplied the formula for acceleration by neglecting the effects of friction, leading to an incorrect velocity calculation of 1.84 m/s.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of friction coefficients (static and kinetic)
  • Familiarity with kinematic equations
  • Basic trigonometry for angle calculations
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  • Calculate net force on an inclined plane with friction
  • Learn about the dynamics of motion on inclined planes
  • Study the effects of different friction coefficients on acceleration
  • Explore advanced kinematic equations for objects in motion with friction
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Students in physics, educators teaching mechanics, and anyone interested in understanding motion dynamics on inclined planes with friction.

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Homework Statement



A block with a mass of 1.137 kg is placed at the top of an inclined plane. The plane is d = 2.592 m long. The angle θ the plane makes with the horizontal can be adjusted, changing the height of the top of the plane.

The lower half of the plane has a rough surface with μs = 0.417, μk = 0.375, while the top half of the plane is smooth with μs' = 0.135, μk' = 0.087. These coefficients are given between the plane and the block.

The block is placed at rest at the very top of the slope. What minimum angle should the slope be set for the block to just start sliding downwards?

I calculated the angle to be 7.688 degrees (which is been accepted as correct)

Now I need to calculate - The slope is held at this angle and the block slowly accelerates from rest down the slope. What is the speed of the block halfway down the slope?

The Attempt at a Solution



Vf^2 - Vi^2 = 2as

Vf^2 = 2 x (9.8m/s x sin(7.688) x 1.296m
= 3.398
sqrroot = 1.84m/s

But this is incorrect. Can anyone point me in the right direction or let me know what I am not understanding? Thank you in advance! :)
 
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g x sin θ applies only for a frictionless surface.

When there is friction, you must determine the nett force acting along the slope, and use that to calculate accn.
 

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