6. EXTRA CREDIT (10 points) A sled of mass m = 2.0 kg is given a kick at the bot

Question

6. EXTRA CREDIT (10 points) A sled of mass m = 2.0 kg is given a kick at the bottom of an icy slope that makes an angle of 20-degrees with the horizontal. The kick imparts an initial speed Vi at the bottom. The block comes to rest after moving up the incline to a point a distance of d = 5.00 m from the bottom. Assume that the coefficient of kinetic friction is 0.100. (a) (2 points) What is h in the diagram from trigonometry? (b) (2 points) What is the work Wg done by gravity during the motion? (c) (2 points) What is the work Wr done by friction during the motion? (d) (2 points) What is the initial kinetic energy Ki of the sled? (e) (2 points) What is the initial speed Vi of the sled? 20

Explanation / Answer

(A) sin20 = h / d

h = 5 sin20 = 1.71 m

(B) W = - m g h = -2 x 9.8 x 1.71

W = - 33.6 J

(C) f= uk N = 0.10 x 2 x 9.8 x cos20 = 1.84 N

W = - f d = - 9.21 J

(D) Applying work - energy theorem,

net work done = change in KE

- 9.21 - 33.6 = 0 - Ki

Ki = 42.8 J

(E) Ki = m Vi^2 /2

Vi = 6.54 m/s

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