A new event has been proposed for the Winter Olympics. An athlete will sprint 10

Question

A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 24 kg bobsled. The person and bobsled will then slide down a 45-m-long ice-covered ramp, sloped at 20, and into a spring with a carefully calibrated spring constant of 2100 N/m . The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 44 kg , has been training for this event. She can reach a maximum speed of 10 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 44 x 10 * 10 = 2200 J
The vertical height loss on the ramp (h) = 45 x sin20* = 45 x 0.34 = 15.3m
=>Gain in KE = Loss in PE
=>KE(g) = m x g x h = (24+44) x 9.8 x 15.3 = 10195.92 J
Total Energy(E) = KE+KE(g) = 2200+10195.92 = 12395.92 J
By E = 1/2kx^2
=>12395.92 = 1/2 x 2100 x (x)^2
=>x = 3.435m

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