If one of the metal spheres on a Newton’s cradle is pulled back and released the following occurs: 1. The potential energy of the sphere is converted to kinetic energy as it swings down.
2. It strikes the next sphere in the series and almost instantaneously stops.
3. The sphere on the opposite side of the frame takes virtually all of the kinetic energy (or momentum) and immediately swings up in an arc to almost the same height as the first sphere. (In this case, the initial kinetic energy is converted to potential as it slows to a stop before falling again.)
4. This demonstrates that the energy and momentum are conserved in the reaction as the spheres continue to pass on their energy.
QUESTIONS AND ANSWERS
3. A rifle bullet of mass 20 g enters a resting Kevlar (bulletproof) jacket of mass 2 kg at 300 m s−1. Calculate the resulting velocity.
4. Two vehicles are approaching a crossroads. The car of mass 1200 kg is travelling south at 25 m s−1. The second car of mass 1000 kg is travelling east at 30 m s−1. If they coalesce on impact, calculate the resultant velocity.
Solution
First draw a momentum vector diagram (Fig. 4.15):
FIG. 4.15
1st car: p = mv ⇒ p 1 = (1200)(25) = 30 000 kg m s−1 south
2nd car: p = mv ⇒ p 2 = (1000)(30) = 30 000 kg m s−1 east
Resultant momentum: √
= 42 426.4 kg m s−1 Resulting velocity: 42 426.4
(30 000)2 + (30 000)2
___________ 2200 = 19.29 m s−1
Resulting direction: tan q = 30 000
_________ 30 000 ⇒ q = 45°
Final resultant velocity = 19.29 m s−1 south-east You may now complete Exercise 4B (page 44).
You may now proceed with the mandatory experiment: Verification of the principle of conservation of momentum (page 411).
36 FUSION ___________________________ 30 000 kg m s–1 east 30 000 kg m s–1 south
FIG. 4.14 A Newton’s cradle demonstrates the conservation of momentum
NOTE
There is some energy lost from the system as sound/heat in every collision. This explains the eventual drop in height reached and final stop of the sequence
