1) You (m=76kg) find yourself on a sled (m-2kg) in the snow, and at the top of a
ID: 2031432 • Letter: 1
Question
1) You (m=76kg) find yourself on a sled (m-2kg) in the snow, and at the top of an 8m tall hill. You carefully (and slowly) nudge yourself off the edge of the hill and start down the 15-degree incline. There is some friction between the sled and the snow (?-0.1). Right when you transition from the hill to flat ground you find that someone has constructed and wall with a giant horizontal spring attached to it. You hit it and it brings you to a stop in 2.1m and then sends you back up the hill. What is the spring constant of the spring?Explanation / Answer
sin15 = h/L
length of slope = h/sin15 = 8/sin15 = 31 m
M = m+m = 76 + 2 = 78 kg
compression in spring x = 2.1 m
initial gravitational potential energy at the top Ug1 = M*g*h
final gravitational potential energy at the flat surfcae U2 = 0
work done by friction Wf = -u*M*g*costheta*(L+x)
initial energy stored in spring Ue1 = 0
final energy stored in spring Ue2 = (1/2)*k*x^2
initial kinetic energy K1 = 0
final kinetic energy K2 = 0
total work done = change in KE
Wg + Wf + We = K2 - K1
Ug1 - Ug2 + Wf + Ue1 - Ue2 = 0
M*g*h - u*M*g*costheta*(L+x) - (1/2)*k*^2 = 0
78*9.8*8 - 0.1*78*9.8*cos15*(31+2.1) - (1/2)*k*2.1^2 = 0
spring constant K = 1665 N/m
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