A new event has been proposed for the Winter Olympics. As seen in the figure, an

Question

A new event has been proposed for the Winter Olympics. As seen in the figure, 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 degree, 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 in dash. (a) How far will Lisa compress the spring? (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?

Explanation / Answer

a)

Conserving momentum for Lisa/sled system :

40*12 = (40+20)*u

So, u = 8 m/s

Now, the height descended by Lisa : h = 50*sin(20 deg) = 17.1 m

So, KE increase for Lisa/sled system = 0.5*mu^2 + m*gh <---------- m = (40 + 20) kg

So, by onservation of energy, all the KE at the start of compression of the spring must be converted to PE stored in the spring

So,  0.5*mu^2 + m*gh = 0.5*kx^2

So, 0.5*(60)*8^2 + 60*9.8*17.1 = 0.5*2000*x^2

So, x = 3.46 m <------answer

b)

The shape of the ramp is not important but rather the angle of the slope determines the final speed of the Lisa/sled system.

So, angle of the slope is only important

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