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Analyzing Incline Problems

Analyzing Incline Problems. Similar to Equilibrium Problems: Pick the object you are analyzing Draw Free-Body-Diagram with all forces to scale Assign a coordinate plane (Make it Convenient!) List all forces in x-direction List all forces in y-direction ∑ F x = ∑ m∙ a x ∑ F y = ∑ m∙ a y

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Analyzing Incline Problems

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  1. Analyzing Incline Problems • Similar to Equilibrium Problems: • Pick the object you are analyzing • Draw Free-Body-Diagram with all forces to scale • Assign a coordinate plane (Make it Convenient!) • List all forces in x-direction • List all forces in y-direction • ∑Fx= ∑m∙ax • ∑Fy = ∑m∙ay • Solve the system of equations Sample Problem: (From Textbook) A 205 kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at 30.0o to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.900, and the log has an acceleration of 0.800 m/s2. Find the tension in the rope.

  2. Solution to Sample Problem • First, find the weight of the log: Fg = mag = (205 kg)(10 m/s2) = 2050 N • Next, find the x- and y-components of the weight: Fg,x = Fgsinθ = (2050 N)sin(30) = 1025 N Fg,y= Fgcosθ= (2050 N)cos(30) = 1775 N • Force of Friction: Ff = μFN = μFg,y = (0.900)(1775 N) = 1598 N • All the forces pulling up the incline: • Tension • All the forces pulling down the incline: • Friction, x- component of gravity • Rearrange to solve for Tension Force! +y FN +x FT Ff Fg,y Fg Fg,x • ΣFx = Σm∙ax • FT – Ff – Fg,x = max • FT= Ff+ Fg,x+ max • = (1598 N) + (1025 N) + (205kg)(0.8 m/s2) • = 2787 N

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