(Non/)Equlibrium and Newton's Laws of Motion

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SUMMARY

The discussion centers on calculating the acceleration of a crate sliding down a ramp inclined at 33.6° with a coefficient of kinetic friction of 0.485. The key equation derived is a = gsin(θ) - μgcos(θ), where g is the acceleration due to gravity (9.8 m/s²). Participants clarify that mass can be treated as a variable that cancels out, allowing for a simplified approach to solving the problem. The final acceleration formula is confirmed as correct by the participants.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Familiarity with the concepts of friction and inclined planes
  • Basic algebra for manipulating equations
  • Knowledge of trigonometric functions (sine and cosine)
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  • Study the derivation of forces on inclined planes in physics
  • Learn about the role of friction in motion dynamics
  • Explore the application of Newton's second law in various contexts
  • Practice solving problems involving different angles and coefficients of friction
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of applying Newton's Laws to real-world scenarios.

Gannon
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This is mainly stumping me because of the absence of any force or mass.

Homework Statement



A crate is sliding down a ramp that is inclined at an angle of 33.6° above the horizontal. The coefficient of kinetic friction between the crate and the ramp surface is 0.485. Find the acceleration of the moving crate.

[tex]\mu[/tex][tex]_{k}[/tex]= .425
[tex]\theta[/tex] = 33.6
g = 9.8m/s[tex]^{2}[/tex]

Homework Equations



Well, F[tex]_{net}[/tex]x = ma , but there is no mass... I don't know where to go from here. :frown:

Any help is appreciated. Thanks.
 
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If you think about the ideal concepts of this type of motion, you can see that mass does not matter. Start to solve the equation as if you had a mass (just use 'm' in place of the unknown quantity) and you'll see it's not as important as you think. If you get stuck in the actual solving, post again with your progress.

Bryan
 
Ok... I think I'm on the right track. So the net force will be simply

mgsin[tex]\theta[/tex] - [tex]\mu[/tex]mgcos[tex]\theta[/tex] = ma

You can divide everything by mass, leaving

gsin[tex]\theta[/tex] - [tex]\mu[/tex]gcos[tex]\theta[/tex] = a.

Is this correct?
 

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