A new event has been proposed for the Winter Olympics. As seen in the figure, an

Question

A new event has been proposed for the Winter Olympics. As seen in the figure, 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 training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash.

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

b) The energy of the sled does not depend on the slope of the incline, only on the height.

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