Yelena Isinbayeva (53.6 kg) at a point in her vault where the pole is maximally
ID: 1424660 • Letter: Y
Question
Yelena Isinbayeva (53.6 kg) at a point in her vault where the pole is maximally deflected (x = 1.58 m). The pole has a bending stiffness of 1149 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 4.49 m/s and she is 2.60 m above the ground.
Assume the vaulter lands on a mat whose top surface is 1 m above the ground and that the mat deforms by 0.5 m in bringing the vaulter to a complete stop. How much work was done on the vaulter by the mat?
The correct calculated values I have are
Potential energy: 1367.12J
Kinetic Energy: 540.29J
Stored energy: 1434.18J
Time to fall from max height to the mat: 1.044 seconds
Velocity: -10.24m/s
Yelena Isinbayeva (53.6 kg) at a point in her vault where the pole is maximally deflected (?x = 1.58 m). The pole has a bending stiffness of 1149 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 4.49 m/s and she is 2.60 m above the ground. Assume the vaulter lands on a mat whose top surface is 1 m above the ground and that the mat deforms by 0.5 m in bringing the vaulter to a complete stop. How much work was done on the vaulter by the mat? The correct calculated values I have are Potential energy: 1367.12J Kinetic Energy: 540.29J Stored energy: 1434.18J Time to fall from max height to the mat: 1.044 seconds Velocity: -10.24m/sExplanation / Answer
P=W/t
work done = change in energy
Hooke's Law: Fs=kx
Ws=(1/2)kx2
KE=(1/2)mv2 = 540.29J
PEg=mgh = 1367.12J
SE=(1/2)kx2 = 1434.18J
Total energy = KE+PE+SE = 540.29+1367.12+1434.18
= 3341.59J
But make it -3008.82 because it is opposite the direction Yelena is travelling.
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