You and a friend are sitting on skateboards on the top of a hill. You are in fro
ID: 1362907 • Letter: Y
Question
You and a friend are sitting on skateboards on the top of a hill. You are in front of your friend and your friend holds onto you from behind. The hill has a 20% grade to it. The coefficient of rolling friction for you is r = 0.2 and the coefficient of rolling friction for your friend is r = 0.15. You have a mass of mA = 80 kg whereas your friend’s mass is mB = 100 kg. (a) How long does it take for the two of you to roll 50 m down the hill? (b) How fast are you traveling when you reach the bottom of the hill?
Explanation / Answer
The hill has 20% grade. It means the slope angle = Inverse Tangent (Grade / 100) = 11 degrees =
The force acting on person A could be calculated using the formula : fs = µr N = µr m g sin
Since f = ma = µr m g sin
Acceleration of person A = 80 x a = 0.2 x 80 x sin 11
a = 0.2 x 0.99 = 0.198
Acceleration of person B = 100 x a = 0.15 x 100 x Sin 11
a = 0.15 x 0.99 = 0.149
Acceleration of two persons = average acceleration of both persons A and B = 0.174 m / s2
Time taken by both persons to reach 50m down the hill could be calculated by using the formula :
S = ut + (1/2) a t2 .
The initial velocity = u = 0 m/s
Hence, 50 = 0.5 x 0.174 x t2
t = 23.97 sec.
Velocity of person A and B is the same at the bottom of the hill because they hold each other.
V = S / t = 50/23.97 = 2.085 m/s
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