What it shows
In a collision the total momentum of two cars is the same before and after, even though some kinetic energy is lost. Slow-motion video gives the speeds.
The science
Momentum p = m v is conserved when no external force acts on the system, here the two cars during the brief collision. So m1 u1 + m2 u2 = m1 v1 + m2 v2. In a perfectly inelastic collision the cars stick and the final speed is (m1 u1 + m2 u2) / (m1 + m2), and the kinetic energy falls. In a nearly elastic collision with a spring bumper the kinetic energy is nearly conserved too. Friction on the table slowly slows the cars but is small during the collision.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Two toy cars of known mass (weigh them on a kitchen scale)
- A smooth table or a long plank with a marked 1 cm grid
- Blu-tack or Velcro to make them stick, and a spring or rubber band for a bounce
- A phone camera with slow motion (120 or 240 frames per second)
- A metre rule laid on the table in the picture
- A notebook and a calculator
Safety
For this project: Keep the cars away from the table edge and from the floor beneath it. An adult must supervise small parts.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Weigh both cars and tape a ruler along the track so that it shows in the video.
Place car 2 at rest in the middle and give car 1 a push toward it; film the collision from above in slow motion.
Play the video frame by frame and read the position of car 1 over several frames before the collision to get its speed u1.
Find the speeds just after the collision v1 and v2 in the same way, from positions and frame times.
Calculate the total momentum before and after, and the kinetic energy before and after.
Repeat for a sticky collision with Blu-tack on both cars and for a spring bounce.
Repeat with a heavier car 2 loaded with coins and fill a table of momentum and energy for each case.
What you should see
The total momentum before and after is equal within about 10 percent in every case. Kinetic energy is almost conserved for the spring bounce but falls by about half or more for the sticky collision.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the law of conservation of momentum?
The total momentum of a system is constant if no external force acts on it.
2What kind of collision conserves kinetic energy?
An elastic collision.
3Where does the lost kinetic energy go in a sticky collision?
Into heat, sound and the deformation of the cars.
4Why does the heavier car move slowly after being hit?
For the same momentum change a larger mass has a smaller change of speed.
Take it further
Start with both cars at rest, joined by a compressed spring, release them and show that the two momenta are equal and opposite.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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