A now event. shown in. has been proposed tot the Winter Olympics. An athlete wil

Question

A now event. shown in. has been proposed tot the Winter Olympics. An athlete will sprint 100 m. starts 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 degree. and into a spring with a carefully calibrated spanning 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 training tor this event She can reach a maximum speed of 12 m/s in the 100 m dash. How far will Lisa compress the spring?

Explanation / Answer

KE of the Lisa = 1/2 x m x v^2 = 1/2 x 40 x 12 x 12 = 2880 J

The vertical height loss on the ramp (h) = 50 x sin20* = 50 x 0.34 = 17m

=>Gain in KE = Loss in PE

=>KE(g) = m x g x h = (20+40) x 9.8 x 17 = 9996 J

Total Energy(E) = KE+KE(g) = 2880+9996 = 12876 J

By E = 1/2kx^2

=>12876 = 1/2 x 2000 x (x)^2

=>x = sqrt12.876 = 3.59m

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