11 A new event has been proposed for the Winter Olympics. As seen in FIGURE P10.

Question

11 A new event has been proposed for the Winter Olympics. As seen in FIGURE P10.54, an athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-covered ramp, sloped at 20° and into a spring with a carefully calibrated spring constant of 2000 N/m·The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been train- ing for this event. She can reach a maximum speed of 12 m/s in the 100 m dash. a. How far will Lisa compress the spring? b. The Olympic committee has very exact specifications about TACTICS O The dis The dis transfo down e A poin 0 The pa e The P the shape and angle of the ramp. Is this necessary? What fac- tors about the ramp are important? consta raise the Pl 20° FIGURE P10.54

Explanation / Answer

for the given frictionelss setup

a. lisa's speed before hitting bobsled, v = 12 m/s
mass = m = 40 + 20 kg
hence
KE = 0.5mv^2

potential energy gained due to falling of the height ,h = L*sin(theta)
here L = 50 m, theta = 20 deg

hence
total KE before copmpressing the spring = 0.5mv^2 + mgLsin(theta)
net cpomperssion of the spring = x
from conservation of energy
0.5kx^2 = 0.5mv^2 + mgLsin(theta)
k = 2000 N/m
3.792 m

b. as only Lsin(theta) is important, so the olympic comittee can choose any combination of L ans theta to keep Lsin(theta) constant for the evemt

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