A new generation of pogo sticks lets a rider bounce more than 2 meters off the g

Question

A new generation of pogo sticks lets a rider bounce more than 2 meters off the ground by using elastic bands to store energy. When the pogo's plunger hits the ground, the elastic bands stretch as the pogo and rider come to rest. At the low point of the bounce, the stretched bands start to contract, pushing out the plunger and launching the rider into the air. For a total mass of 80 (rider plus pogo), a stretch of 0.40 launches a rider 2.0 above the starting point.

Assuming that the elastic bands stretch and store energy like a spring, how high would the 80 pogo and rider go for a stretch of 0.20 ?

a.) 2.0 m
b.) 0.50 m
c.) 1.0 m
d.) 1.5 m

A pogo and rider of 80 total mass at the high point of a 2.0 jump will drop 1.4 before the pogo plunger touches the ground, slowing to a stop over an additional 0.40 as the elastic bands stretch. What approximate average force does the pogo stick exert on the ground during the landing?

a.) 4000 N
b.) 2800 N
c.) 1400 N
d.) 700 N

Explanation / Answer

Assuming that the elastic bands stretch and store energy like a spring by energy conservation, mgh = 1/2kx^2 => 80*10*2 = 0.5*k*0.4^2 => 1600 = 0.08k =>k = 20000 now, for a stretch of 0.20m mgh = 1/2kx^2 => 80*10*h = 0.5*20000*0.2^2 => h = 400/800 => h = 0.50m b.) h =0.50m b. approximate average force does the pogo stick exert on the ground during the landing = mg + 1/2kx^2 = 80*10 + 1/2*20000*0.16 = 2400N

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