A new event has been proposed for the Winter Olympics. An athlete will sprint 10
ID: 1322030 • Letter: A
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 50-m-long ice covered ramp, sloped at 20?, and into a spring with a carefully calibrated spring constant of 2300 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.
(a) How far will Lisa compress the spring?
m
(b) The Olympic committee has very exact specifications about the shape and angle of the ramp. Is this necessary? What factors about the ramp are important? (Select all that apply.)
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
(40 kg)(12 m/s) + (20 kg)(0 m/s) = (40 + 20 kg)vf
vf = 8.0 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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