You and your friends push a 75-kg greased pig up an aluminum slideat the county
ID: 1752751 • Letter: Y
Question
You and your friends push a 75-kg greased pig up an aluminum slideat the county fair, starting from the low end of the slide. Thecoefficient of kinetic friction between the pig and the slide is0.070. (a) All of you pushing together (parallel tothe incline) manage to accelerate the pig from rest at the constantrate of 4.3 m/s2 over adistance of 1.5 m, at which point yourelease the pig. The pig continues up the slide, reaching a maximumvertical height above its release point of 60 cm. What is the angle of inclination of theslide?°
(b) At the maximum height the pig turns around and begins to slipdown the slide, how fast is it moving when it arrives at the lowend of the slide?
m/s (a) All of you pushing together (parallel tothe incline) manage to accelerate the pig from rest at the constantrate of 4.3 m/s2 over adistance of 1.5 m, at which point yourelease the pig. The pig continues up the slide, reaching a maximumvertical height above its release point of 60 cm. What is the angle of inclination of theslide?
°
(b) At the maximum height the pig turns around and begins to slipdown the slide, how fast is it moving when it arrives at the lowend of the slide?
m/s
Explanation / Answer
s = .5at^2 s = 1.5 m a = 4.3m/s^2 t = time of push-up Speed the pig gained after 1.5 m : v = at, v^2 = 2ax KE = .5mv^2 L = h/sin h = 60 cm = .60 m, =what we are trying to figure out PE = mgh f = w1; w1 = mgcos -> so f = mgcos fL = .5mv^2 - mgh -> ughcos/sin = as -gh cot = (as -gh)/(gh) =tan^-1(gh/(as-gh)) = tan^-1(.070 x 9.8 x.60)/(4.3x1.5-9.8x.60) = 35.8 degrees Part b) Potential energy above the low end of the ramp: W = mg((s)(sin) + h) Pig's ramp position : p = s+L = s+h/sin Final kinetic energy W1 = W - W2, W2 = fp W1 = .5mv^2 -> .5mv^2 = mg(ssinb +h) - mgcos(s +h/sin) v^2 = 2g(ssin + h)(1-cot) v^2 = 2x9.8x1.5xsin35.8 + .6 x (1-.07cot35.8) v = 5.11 m/s
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