Weird Defensive Force Field of Alien Space Probe

[pkwhitey]

In a rather bad science fiction movie, astronauts Susie (mass 60 kg) and Fred (mass 86 kg) are investigating an alien probe. All of a sudden, the probe starts to produce a weird defensive force field. Their space ship's board computer scans the field and produces the above plot of the potential energy that Susie and Fred would have at different distances from the probe. The potential continues to be zero at larger distances than shown.

The computer locates Susie drifting toward the probe at a distance of 5 m with a total (mechanical) energy of 7 kJ, and Fred, also drifting toward the probe, at a distance of 6 m with a total (mechanical) energy of 9 kJ. One Kilojoule (kJ) is 103 Joules.

1.) What will be Fred's maximum speed?
2.) What will be Fred's final speed?

E[SUB m]=K+U K=(1/2)mv^2 How I began Solving: I began by using what is given to find out how much potential energy Fred had. I know that the maximum speed will occur by using one of the turning points on the graph. I am not sure though how to use the information given to find the maximum speed and final speed.

Thank You.

 

[haruspex]

It might help you to think about it if you model it in a simple Earthbound context. How might you set up a potential energy curve like that?

 

[pkwhitey]

It might help you to think about it if you model it in a simple Earthbound context. How might you set up a potential energy curve like that?

Well I know that the the maximum speed occurs when the potential energy is at its minimum. The potential energy is at a minimum at x=5m. I am looking for the maximum velocity but I don't know how to find the kinetic energy at the point.

 

[haruspex]

Well I know that the the maximum speed occurs when the potential energy is at its minimum. The potential energy is at a minimum at x=5m. I am looking for the maximum velocity but I don't know how to find the kinetic energy at the point.

Yes, the max speed will be at minimum PE. That follows from a certain conservation law. That law tells you more than just that, though. What is that law in full?

 

[pkwhitey]

Yes, the max speed will be at minimum PE. That follows from a certain conservation law. That law tells you more than just that, though. What is that law in full?

Ok, I understand. E_M= U+K U=-8kJ and E_M=9kJ 17kJ=.5mv^2 solve for v.

Thank you.