1.1b – Example how high, how fast answers
Q1) An archer firing an arrow
a) What questions could you ask about this situation
that could be answered by energy analysis? What stores are involved and how do
they change over time?
Two questions that could be meaningfully asked and potentially calculated for this situation are
- How Stretched (energy in the elastic store of bow decreases) → How Fast (energy in the kinetic store of arrow increases)
- (If firing upwards) How Stretched (energy in the elastic store of bow decreases) → How High (energy in the gravitational store of arrow increases)
Some students may suggest How Stretched → How Far and this is a reasonable and interesting question. This is beyond the scope of the stores and pathways model and motion analysis studies at this level. It can, however, be answered with ideas studied at higher levels and so you may wish to explain to students that more complex analysis is possible, and interesting.
b) State some sensible start and end points for the
analysis.
How Stretched → How Fast: The start point would be when the arrow is pulled back fully, just before the archer releases their grip. The end point would be at the point where the arrow flies off and just as it is no longer in contact with the bow string.
How Stretched → How High: The start point would be when the arrow is pulled back fully, just before the archer releases their grip and fires the arrow upwards. The end point would be at the highest point of the path of the arrow where it is changing direction.
Students sometime think that objects continue to accelerate after they have been fired (or kicked) but this is not the case. Once they are no longer in contact, there is not an accelerating force and so they begin to slow down. This is a common misconception, and is associated with other confusion around Newton’s first law (see Forces module, 5.2 Subject knowledge - Newton's Laws.
Q2) An athlete pole vaulting
a) During the run up what questions could you ask about this situation
that could be answered by energy analysis? What stores are involved and how do
they change over time?
Four questions that could be meaningfully asked and potentially calculated for this situation are
- How Fast (kinetic store of athlete decreases) → How Stretched (elastic store of pole increases)
- How Stretched (elastic store of pole decreases) → How High (gravitational store of athlete increases)
- How Fast (kinetic store of athlete decreases) → How High (gravitational store of athlete increases)
- How High (gravitational store of athlete decreases) → How Fast (kinetic store of athlete increases)
b) State some sensible start and end points for the analysis.
How Fast → How Stretched (during the run up to just before they lift off). The start point is when they are at maximum speed on the run up. The end point is when the pole is most bent and the athlete is just starting to take off.
How Stretched → How High (ground to top of jump). The start point is when the pole most bent and the athlete is just starting to take off. The end point is when they are at their maximum height.
How Fast → How High (run up to top of jump). The start point is when they are at maximum speed on the run up. The end point is when they are at maximum height.
How High→ How Fast (from top of jump to just before they land). The start point is when they are at their maximum height. The end point is when they are just about to touch the safety mat at the end of their fall.
Q3) A car applying its brakes
a) What questions could you ask about this situation
that could be answered by energy analysis? What stores are involved and how do
they change over time?
One question that could be meaningfully asked and potentially calculated for this situation is How Fast (kinetic store of car decreases) → How Hot (thermal store of brakes increases)
b) State some sensible start and end points for the analysis.
How Fast → How Hot. The start point would be just before the brakes are applied. The end point would be when the car has stopped moving (and the brakes are still red hot).
How Fast → How Far. The start point would be just before the brakes are applied and he end point would be when the car has stopped moving.
During the braking process, the brakes will be cooling and heating the air around them and so this calculation will not give a precise value, however it will give a maximum value against which the brakes would need to be designed. It could also lead on to discussion, from an engineering context, on braking systems that have cooling systems built in. This principle can be shown to students with an electric drill when it drills into wood and smoke can sometimes be seen.
In all cases these questions assume or imply a perfectly efficient transfer between the stores, and this is almost certainly not likely to be the case. As such, any value for the second energy store (the one that increases) provides a maximum possible value, which could not be exceeded without violating the law of conservation of energy.
1.1a – Example how high, how fast questions