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 20 kg bobsled. The person and bobsled will then slide down a 55-m-long ice-covered ramp, sloped at 20 degree, and into a spring with a carefully calibrated spring constant of 2500 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 36 kg, has been training for this event. She can reach a maximum speed of 15 m/s in the 100 m dash. How far will Lisa compress the spring? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

u = 15m/s
hieght lost on bobsled = lsin(20) = 55*sin(20) = 18.811 m
p.e. lost = mgh = (36+20)*9.8*18.811 = 10323.536 J = ke gained

hence final ke = initial ke + p.e lost ......(1)

Now to find initial ke, let the combined velocity of cart and athlete after 100 m dash be u'
then
36*15 = (36 + 20)u' [ conservation of momentum]
u' = 9.642 m/s

initial ke = 0.5(20+36)u'^2 = 2603.571 J
final ke (from 1) = 2603.571 + 10323.536 = 12927.107 J
energy stored by spring = 0.5kx^2 = 12927.107 (conservation of energy)
x = 3.215 m

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