The Bobsled Jump will be a new event at the 2014 Winter Olympic Games in Sochi,

Question

The Bobsled Jump will be a new event at the 2014 Winter Olympic Games in Sochi, Russia. The bobsleds (and occupants) are launched (at point A) by a largespring onto a huge semi-circular track (radius=100m) of frictionless ice, as shown below. The bobsled teams try to achieve the furthest landing distance on a level landing field below.

A.) Find the work (if any) done by the ramp on the bobsled as it moves from point A to point B. Explain your reasoning.

B.) The mass of the Jamaican team (including bobsled) is 800 kg. If they are traveling at a speed of vB=50 m/s when they reach point B, find the spring constant for the spring. (The spring was compressed x=4.0 m before the launch.)

C.) Find the accleration of the bobsled (magnitude and direction) at point B.

D.) Find the magniutde of the normal force by the track on bobsled at point B.

E.) How fast will the Jamaican team be traveling right before they land on the landing field? Will this hurt?

Please show the work to how to get these answers!

Explanation / Answer

A)

W = -(mgH+1/2kx^2)

Potential energy decreases as bobsled move from A to B. and is give by mgH

as this work is done by gravity and spring force so,, work done by bobsled =-(mgH+1/2kx^2)

B)

mgH+1/2kx^2 = 1/2*mv^2

k = (0.5*800*50*50-800*9.81*100)/8 = 26900 N/m

C)

v^2 = u^2+2as

u=0

a = v^2/(2*s) = 50*50/(2*(100+4) = 12.0192 m/s^2

D)

N = mg = 800*9.81 = 7848 N

E)

1/2m*V^2 = 0.5*mv^2+mg*20

V = sqrt((0.5*800*50*50+800*9.81*20)/(0.5*800)) = 53.781 m/s

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