A new event has been proposed for the Winter Olympics. An athlete will sprint 10

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 44 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?

(b) The Olympic committee has very exact specifications about the shape and angle of the ramp. Is this necessary? If the committee asks your opinion, what factors about the ramp will you tell them are important? (Select all that apply.)

vertical descent

color

angle

shape

friction

Explanation / Answer

a] The momentum of the system (Lisa and bobsled) is conserved before and after she jumps onto it.

Mu + 0 = (m+M)V

44(12) = (44+20)V

=> 8.25 m/s

this is the collective speed of Lisa-bobsled before they begin their descent from the slope.

Since the slope is ice covered, it can be assumed to be frictionless. The height of the descent will then be:

H = Lsin20 = 50sin20 = 17.101 m

therefore, Initial energy = (1/2)(M+m)V2 + (M+m)gH = (1/2)(64)(8.25)2 + (64)(9.8)(17.101) = 12903.75 J

now, using conservation of energy, this will be the final energy at the ground level.

Also, since there is no loss in energy due to friction anywhere, this energy will be the energy stored in the spring when it compresses.

so, 12903.75 = (1/2)kx2

=> 12903.75 = (1/2)(2300)x2

=> x = 3.35 m.

this is how far Lisa compresses the spring.

b]

Since the compression of the spring was Energy dependent which was Height dependent (due to the potential energy), therefore, the angle of the slope is inconsequential. The vertical descent is important for the ramp, not the inclination.

Also, if the friction of the ramp is non-zero, some amount of initial energy is lost while traveling down the slope thereby changing the compression length of the spring. So, the friction of the ramp also matters.

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