Hint: This problem requires a train of logic. (1) Analyze force diagram, (2) use

Question

Hint: This problem requires a train of logic.

(1) Analyze force diagram,

(2) use Newton%u2019s Laws, and

(3) solve the equations of motion.

A block starts from rest at a height of 3.1 m on a %uFB01xed inclined plane. The acceleration of gravity is 9.8 m/s2

Block wieghs 6.4 kg

u = 0.22

angle=26 degrees

What is the speed of the block at the bottom of the ramp?Answer in units of m/s

If the block continues to slide on the groundwith the same coe%uFB03cient of friction, how farwill the block slide on the ground until coming to rest?Answer in units of m

Explanation / Answer

m*g*sin(26) = tendency to move down the incline = 6.4*9.8*0.438 N = 27.5 N

0.22*m*g*cos22 = maximum force of friction = 12.8 N

So, the net force down the incline is 27.5 N - 12.8 N = 14.7 N

a = 14.7/6.4 = 2.3 m/s^2

Thus, using v^2 = u^2 + 2as

and s = L / sin22 = 3.1/sin22 m = 8.28 m

u = 0

So, v = (2*2.3*8.28)^0.5 m/s = 6.17 m/s

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