A pole vaulter (mass = 75kg) sprints down the track and hits a speed of 10m/s at

Question

A pole vaulter (mass = 75kg) sprints down the track and hits a speed of 10m/s at the instant she plants the pole in the "box" (->Ek). The vaulter expends 4000J (=Ec) of energy sprinting down the track. The pole bends 4m and has a spring constant of 400N/m (->Eel). The vaulter achieve a maximum height of 4.2m (->E­g). The final velocity of the vaulter just before hitting the mats is 9m/s (thermal energy has been generated during the entire process -> Et) Rank the energy transformation (Ek, Ec, Eel, Eg, Et) from largest to smallest. (please explain)

Explanation / Answer

the kinetic energy of vaulter is

Ek = (1/2) mv^2 = (1/2) ( 75 kg) ( 10 m/s)^2 = 3750 J

Ec = 4000 J

eleastic potential energy is

E el = ( 1/2) kx^2 = (1/2) ( 400 N/m) ( 4 m)^2 = 3200 J

grvitational energy is

Eg = mgh = ( 75 kg) ( 9.8 m/s^2) ( 4.2 m ) = 3087 J

theremal energy is

Et = Ek + Eel = 3750 J + 3200 J = 6950 J

the transformation from largest of smallest is

Et >Ec > Ek > Eel > Eg

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