Negative potential wells and escape speed

Science · Forces & Motion · ages 16-18

Name ______________________ Date ____________

Gravitational potential near a planet is negative.
Circle one: True False
Where is gravitational potential defined as zero?
- At infinity
- At the surface
- At the centre
How is escape speed found?
- Divide the weight by the mass
- Set kinetic energy equal to the well depth
- Multiply g by the radius
A craft is lifted from the surface to orbit. What is the sign of its potential energy change?
- Positive, since work is done against gravity
- Negative, since height always lowers energy
- Zero, since gravity does no work
A 2 kg rock sits where potential is minus 5 J/kg. U equals m V. Give U in joules.
Answer: ______________
Why must positive work be done to separate two masses?
- Separation lowers the energy further
- Gravity pulls them together, so they climb toward zero
- Distance has no effect on energy
Two planets share one mass. Planet X is smaller. From which surface is escape speed greater?
- The larger planet, since there is more ground to push from
- Both give the same escape speed
- Planet X, since the well is deeper at smaller R
A satellite with negative total energy will escape Earth.
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · Every finite spot sits below the zero at infinity.
At infinity · Infinity is the agreed zero, so all finite values sit below it.
Set kinetic energy equal to the well depth · The launch energy must exactly fill the well.
Positive, since work is done against gravity · Climbing out of the well raises the energy toward zero.
-10 · Multiply 2 by minus 5 to get minus 10 J.
Gravity pulls them together, so they climb toward zero · Parting bound masses climbs from negative toward zero.
Planet X, since the well is deeper at smaller R · Smaller R deepens minus G M over R, so more kinetic energy is needed.
False · Negative total energy means bound; escape needs zero or more.