Big Air 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 80kg (rider plus pogo), a stretch of 0.40 m launches a rider 2.0 m above the starting point. Assuming that the elastic bands stretch and store energy like a spring, how high would the 80 kg pogo and rider go for a stretch of 0.20 m? A. 2.0 m B. 1.5 m C. 1.0 m D. 0.50 m

Solution In this problem we have to find the height. Before solving this problem we have take data of given values. Data: Height reached by rider=2 m Stretch of the string=0.40 m Mass of the rider=80 kg Potential energy means energy difference between the energy of an object in the given position and a at the end position where it will come to rest.the energy of an object is because of its position rather than its motion Suppose the rider he has some mass is m, and he is in h position in height. If the acceleration of free fall is g, the weight of the pogo rider is mg. So the total work or energy = force × displacement = mg × h = mgh Potential energy = mgh =(80)*(9.8)*(2) =1600 J The P.E stored in spring at the time of launch P.E=½ k(x)^2 k=2(1600)/(.4)^2 k=20000 N/m Similarly we have to find P.E for string for a stretch of 0.20m P.E1=½ k(x1)^2 =½ (20000)(0.20)^2 =400 J This potential energy will converted into potential energy of rider P.E1=mg(h1) 400 J=(80)(9.8)(h1) h1=(400)/(80)(9.8) = 0.5 m