Practice question · Put in order
Order the energy argument that finds the landing speed of a ball dropped from a height h.
- Cancel the mass from both sides
- As it falls, potential energy converts to kinetic energy with the sum unchanged
- Solve to get v equal to the square root of 2gh, independent of the mass
- At the ground all the energy is kinetic, so set mgh equal to one half m v squared
- At the moment of release all the energy is potential: PE = mgh and KE = 0
Hints
- Conservation lets you relate the start and the end without tracking anything in between.
- The mass appears on both sides of the energy equation, so watch what happens to it.
Show the answer
- At the moment of release all the energy is potential: PE = mgh and KE = 0
- As it falls, potential energy converts to kinetic energy with the sum unchanged
- At the ground all the energy is kinetic, so set mgh equal to one half m v squared
- Cancel the mass from both sides
- Solve to get v equal to the square root of 2gh, independent of the mass
Why
Conservation of energy connects the initial and final states directly, with no need for the equations of motion. The cancellation of m is the famous result that all objects fall alike in the absence of air resistance. Galileo's conclusion, recovered in four lines of bookkeeping.
Practise Energy and Conservation Laws
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