(1) You and a friend are sitting on skateboards on the top of a hill. You are be
ID: 1774135 • Letter: #
Question
(1) You and a friend are sitting on skateboards on the top of a hill. You are behind your friend and hold onto your friend from behind. The hill has a 20% grade to it. The coefficient of rolling friction for you is µr 0.2 and the coefficient of rolling friction for your friend is µr 0.15. You have a mass of mA 80kg whereas your friend’s mass is mB 100kg. (a) How long does it take for the two of you to roll a distance of 50m down the hill (that is along the hypotenuse of the hill, not elevation)? (b) How fast are you traveling when you reach the bottom of the hill?
Explanation / Answer
20% grade means change of 20 feet in elevation over a 100-foot stretch along horizontal
slope = tan= 20/100 = 0.2
sin = 0.2 / [(0.22)+(12)] = 0.196
cos = 0.98
friction acting on me = fA = µmAgcos = 153.82 N
friction acting on friend = fB = µmBgcos = 144.21 N
(mA + mB)gsin - fA - fB = (mA + mB)a
=> a = 0.267 m/s2
Applying conservation of energy,
(KE + PE)i - work done by friction = (KE + PE)f
=> 0 - (fA + fB)*50 = (1/2)(mA + mB)v2 - (mA + mB)*g*(50sin)
=> -14901.5 = 90v2 - 17304.84
=> v = 5.168 m/s
=> at = 5.168
=> 0.267*t = 5.168
=> t = 19.36 s
Therefore, it will take 19.36 s to roll 50m along the hill
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