set into motion up an indlined pliane with an initial speed of v- 7.80 m/\'s (se
ID: 2030857 • Letter: S
Question
set into motion up an indlined pliane with an initial speed of v- 7.80 m/'s (see figure below). The block comes to rest after traveling d-3.00 m along the plane, which is inclined at ar, angle of -30.0. to the horizontal, (a) For this motion, determine the change in the block's kinetic energy. (b) For this motion, determine the change in potential energy of the block-Earth system. (e) Determine the friction force exerted on the block (assumed to be constant) (d) What is the coefficient of kinetic friction?Explanation / Answer
(a) change in kinetic energy = ½m(v2-u2) = 0.5 x 4.8 x (0-7.82) = -146.016 J
(b) change in potential energy = mg(dsin) = 4.8 x 9.8 x 3sin(300) = 70.56 J
(c) from the equation of motion
v2 = u2 + 2as
0 = 7.82 + 2xax3
a = -7.82/6 = -10.16 m/s2
so gsin+gcos = 10.16
gcos = 10.16 - gsin = 10.16 - 9.8sin(300) = 10.16 - 9.8 x 0.5 = 5.26 m/s2
so friction force (mgcos) = 4.8 x 5.26 = 25.248 N
(d) coefficient of kinetic friction () = 5.26/(gcos) = 5.26/(9.8 x cos(300)) = 0.62
= 0.62
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