A new event, shown in (Figure 1) , has been proposed for the Winter Olympics. An

Question

A new event, shown in (Figure 1) , 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 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.

How far will Lisa compress the spring?

Explanation / Answer

using work energy theorem

Work done by gravitational force while moving on the ramp is W = m*g*sin(20)*S =0.5*m*(v^2-12^2)

(40+20)*9.8*sin(20)*50 = 0.5*(40+20)*(v^2-12^2)

speed at the end of the ramp is v = 21.9 m/sec

using law of conservation of energy

0.5*m*v^2 = 0.5*k*x^2

0.5*(20+40)*21.9^2 = 0.5*2000*x^2

x = 3.79 m

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