ActivPhysics%20OnLine

1

• ActivPhysics OnLine
• Problem 5.4 Inverse Bungee Jumper
• Choose xy coordinates in the usual way. y
• x
• upwards y
• downwards - y
• In this problem we are assuming there is no
  friction.

2

• Problem 5.4 Question 1
• Do the simulation.
• Notice (a) the womans gravitational potential
  energy increases as her height above the floor
  increases (b) the springs potential energy
  increases as the spring is stretched
• (c) the womans kinetic energy is maximized when
  she is near the middle of an oscillation.

3

• Problem 5.4 Question 2 Construct an energy
  equation for the womans motion. What is the
  force constant of the spring, k, if her head just
  touches the overhead support without injury?
• The systems total energy E is the sum of
  kinetic energy K, grav. potential energy Ug, and
  the springs potential energy Us.
• E K Ug Us

4

• (This problem is similar to Randall Knights
  Physics for Scientists and Engineers, Example
  10.7 on pages 285-286.)
• E K Ug Us
• Let ye the equilibrium position of the spring,
  i.e. the position at which there is no restoring
  force.
• E m v2/2 mgy
• k (y - ye)2 /2

5

• Since total energy is conserved, the energy of
  the system when she is at the top position y2
  energy of the system when she is at the bottom
  position y1.
• mv22/2 mgy2 k (y2 - ye)2/2
• mv12/2 mgy1 k (y1 -ye)2/2
• Her kinetic energy should be 0 at the top and is
  0 also at the bottom where she is at rest.
• mgy2 k (y2 - ye)2/2
• mgy1 k (y1 -ye)2/2

6

• The gravitational potential energy also must be 0
  at the bottom where y 0.
• mgy2 k (y2 - ye)2/2
• k (y1 -ye)2/2
• k (y1 -ye)2/2 - k (y2 - ye)2/2 mgy2
• k (y1 -ye)2/2 - (y2 - ye)2/2 mgy2
• Substitute in values.
• m 50 kg
• g 10 m/s2

7

• Since the y values are zero at the floor
• y2 4.0 m at the top
• y1 - ye - 3.5 m when the spring is stretched
  and her feet touch the floor.
• At the top the spring is slightly compressed and
• y2 - ye 0.5 m.
• k (-3.5m)2 (0.5m)2
• (2)(50 kg)(4.0m)(10m/s2)
• k 4000 N/ 12 m2

8

• k 333 N/ m
• The simulation only proceeds in steps of 5.0
  N/m. Notice on the simulation if
• k 330 N/ m, her head does not quite reach the
  top, but if k 335 N/ m, then she hits her head
  and is injured.