Finding the Angle of Incline for a Block Sliding Down a Frictionless Surface

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To find the angle of incline for a block sliding down a frictionless surface, the key equation involves gravitational force components and friction. The block, with a mass of 4.5 kg, accelerates down a distance of 3m and reaches a speed of 7m/s at the bottom. The correct formulation should use mgsin(θ) for the gravitational force component along the incline, rather than the coefficient of friction. The presence of friction on the horizontal surface after the incline must also be accounted for in the overall motion. The discussion emphasizes the need to clarify the use of variables and ensure the correct application of physics principles in the calculations.
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Homework Statement



A block (starting from rest) with mass m = 4.5 kg slides down a frictionless incline a distance of d = 3m and then slides across a horizontal floor with friction (the coefficient of friction is Fk = 0.52). The speed of the block at the bottom of the incline is v1 = 7m/s. What is the angle of the incline? (Assume the acceleration was constant.)

Homework Equations


v initial = 0
mgsin(mu) - ƒk = ma

The Attempt at a Solution


I am wondering if I am approaching this correctly.
mgsin(theta) - ƒk = ma
 
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cugirl said:

Homework Statement



A block (starting from rest) with mass m = 4.5 kg slides down a frictionless incline a distance of d = 3m and then slides across a horizontal floor with friction (the coefficient of friction is Fk = 0.52). The speed of the block at the bottom of the incline is v1 = 7m/s. What is the angle of the incline? (Assume the acceleration was constant.)

Homework Equations


v initial = 0
mgsin(mu) - ƒk = ma

The Attempt at a Solution


I am wondering if I am approaching this correctly.
mgsin(mu) - ƒk = ma

I hope you mean mgsinθ.

I would be concerned if you were trying to plug in μ, usually used for the coefficient of friction, as the angle.
 
sorry -- that's what I meant. All the greek letters -- uggh.
 
As to the problem, the equation you have doesn't address the basic acceleration down the incline, if your statement of the problem is correct in saying the incline is frictionless.
 
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