61. A child's pogo stick (Fig. P8.61) stores energy in a spring with a force constant of 2.50 X 104 N/m. At position (x -0.100 m), the spring com- pression is a maximum and the child is momentarily at rest. At position ® (xa = 0), the spring is relaxed and the child is mov- B) %3D %3D ing upward. At position ©, the child is again momentarily at rest at the top of the jump. The combined mass of child and pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the child-stick-Earth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xe. (c) Calculate the speed of the child at x = Figure P8.61 0. (d) Determine the value of x for which the kinetic energy of the system is a maximum. (e) Cal- culate the child's maximum upward speed.
61. A child's pogo stick (Fig. P8.61) stores energy in a spring with a force constant of 2.50 X 104 N/m. At position (x -0.100 m), the spring com- pression is a maximum and the child is momentarily at rest. At position ® (xa = 0), the spring is relaxed and the child is mov- B) %3D %3D ing upward. At position ©, the child is again momentarily at rest at the top of the jump. The combined mass of child and pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the child-stick-Earth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xe. (c) Calculate the speed of the child at x = Figure P8.61 0. (d) Determine the value of x for which the kinetic energy of the system is a maximum. (e) Cal- culate the child's maximum upward speed.
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Transcribed Image Text:61. A child's pogo stick (Fig. P8.61)
stores energy in a spring with a
force
104 N/m. At position @ (x
-0.100 m), the spring com-
pression is a maximum and the
child is momentarily at rest. At
position ® (x = 0), the spring
is relaxed and the child is mov-
constant of 2.50 X
%3D
ing upward. At position ©, the
child is again momentarily at
rest at the top of the jump. The
combined mass of child and
pogo stick is 25.0 kg. Although
the boy must lean forward to
remain balanced, the angle is small, so let's assume the
pogo stick is vertical. Also assume the boy does not
bend his legs during the motion. (a) Calculate the total
energy of the child-stick-Earth system, taking both
gravitational and elastic potential energies as zero for
x = 0. (b) Determine xe. (c) Calculate the speed of the
child at x =
Figure P8.61
0. (d) Determine the value of x for which
the kinetic energy of the system is a maximum. (e) Cal-
culate the child's maximum upward speed.
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