Chapter 1.3 #32. If a body slides on a surface, it experiences friction F (a for

Question

Chapter 1.3 #32. If a body slides on a surface, it experiences friction F (a force against the direction of motion). Experiments show that F = u*N ( Coulomb's law of kinetic friction without lubrication), where N is the normal force (force that holds the two surfaces together; and the constant of proportionality u is called the coefficient of kinetic friction. Assume the body weighs 45 nt ( about 10 lbs) u = 0.20, a = 30 degrees, the slide is 10m long, the initial velocity is zero, and the air resistance is negligible. Find the velocity of the body at the end of the slide. Help me out please with the solution! Thanks for taking your time to read this.

Explanation / Answer

Conservation of energy:

m g h = u N l + 0.5 m v^2

m g (l sin) = u (m g cos) l + 0.5 m v^2

g (l sin) = u (g cos) l + 0.5 v^2

9.81*10*sin30 = 0.2*9.81*cos30*10 + 0.5 v^2

9.81*10*0.5 = 0.2*9.81*0.8660254*10 + 0.5 v^2

v = 8.01 m/s

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