posted by Anonymous .
A new event has been proposed for the Winter Olympics. An athlete will sprint 150.0 m, starting from rest, then leap onto a 20.8 kg bobsled. The person and bobsled will then slide down a 46.0 m long ice-recovered ramp, sloped at á=21.0°, and into a spring with a carfully calibrated spring constant of 1544.0 N/m. The athlete who compresses the spring the farthest wins the gold medal. Jennifer, whose mass is 40.0 kg, has been training for this event. She can reach a maximum speed of 14.7 m/s in the 150.0 m dash. How far will Jennifer compress the spring?
Use a conservation of energy method.
Initial KE + gravitational PE loss = spring potential energy.
(1/2) (m + M) Vo^2 + (m + M) g H = (1/2) k X^2
Vo is the initial velocity after getting onto the bobsled. It is less than 14.7 m/s, because there will be some inelastic energy loss hopping on. You will have to use conservation of momentum to compute Vo.
m*(14.7) = Vo*(M+m)
H is the vertical distance her bobsled slides before hitting the spring, 46.0 m * sin 21.
m is her mass (40 kg), M is the bobsled mass (20.8 kg), and g is the acceleration of gravity.
Solve for X