A new Olympic sport called bob sled spring compression will be introduced at the

Question

A new Olympic sport called bob sled spring compression will be introduced at the next Winter Olympics. A 60-kg athlete will sprint 80 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 60 m long ice covered ramp, sloped at 20 degrees, and into a spring with a carefully calibrated spring constant of 2500 N/m. The athlete who compresses the spring the farthest wins a gold medal.

A) If this athlete can reach a max speed from rest to 80 m in a time of 15 seconds, how far will he/she compress the spring?

Explanation / Answer

  First we need to find the speed of Lisa and the bobsled as soon as she jumps on. This can be considered a completely inelastic collision, since she stays on the bobsled. Use the conservation of momentum equation:
m1v1i + m2v2i = (m1 + m2)vf
(60 kg)(80/15 m/s) + (20 kg)(0 m/s) = (60 + 20 kg)vf
vf = 4.25 m/s

Now we can find how much Lisa and the bobsled will compress the spring. This problem is easiest to solve using conservation of energy with springs:
(KE + PEg + PEs)i = (KE + PEg + PEs)f
We can cross out PEsi, KEf, and PEgf because those are zero.
KEi + PEgi = PEsf
1/2 mv^2 + mgh = 1/2 kx^2
sin(20

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