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

Apply law of conservation of momentum:

.                mu=(m+m1)v

.              v=40*12/60=8 m/s

Use the conservation of energy.

0.5(m+m1)v^2+(m+m1)(g)(sin 20)(h)=0.5kx^2
here, m is lisa's mass, m1 is the bobsled, g is gravity, and h is length of the ramp.

Here, the actual height is,

h=50sin 20

Solve for x.

0.5(m+m1)v^2+(m+m1)(g)=0.5kx^2

0.5(60)*8^2+(60)(9.8)(sin 20)(50sin20)=0.5(2000)x^2
x= 3.46 m

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