Moving About

1. Moving About Focus 4: Momentum and Force

2. Outcomes Explain how change of momentum relates to forces acting on the vehicle or the driver. • Define momentum as p = mv • Define impulse as the product of force and time • Solve problems and analyse secondary data using p = mvand Impulse = Ft • Explain why momentum is conserved in collisions in terms of Newton’s 3rd Law of Motion • Perform first-hand investigations to gather data and analyse the change in momentum during collisions • Solve problems that apply the principle of conservation of momentum to qualitatively and quantitatively describe the collision of a moving vehicle with: • a stationary vehicle • an immoveable object • another vehicle moving in the opposite direction • another vehicle moving in the same direction

3. Define Momentum • Momentum is a measure of how hard an object is to stop. • An object moving faster is harder to stop than an object moving slower • A heavier object is harder to stop than a lighter object • This is expressed mathematically by p = mv • p = momentum measured in kgms-1 • m = mass measured in kg • v = velocity measured in ms-1

4. Define Impulse • Impulse is the affect of a force during a particular time. • Mathematically it is defined as I = Ft • I is impulse measured in Ns (Newton-seconds) • F = force measured in Newtons • t = time measured in seconds. • Impulse is the reason you move your hands backwards a bit when catching a set of keys or a cricket ball – you try to make the force act over a longer time.

5. Relationship between Impulse and Momentum • Impulse can also be seen as the change in momentum of an object. • Since “change in” means final minus initial, p = pf– pi p = mv– mu Usually the mass of an object remains the same therefore p = m(v – u) I = Ft So Ft = m(v –u)

6. Momentum and Newton • On the previous slide we had Ft = m(v –u) • This could be rearranged to read • But is acceleration! • So the equation we have is equivalent to F = ma This is how Newton actually got to his second law.

7. Conservation of Momentum • If you take all the forces acting on a system into account, momentum is always conserved • This means that in the absence of an “outside force” the total momentum before an event (eg a collision) is equal to the total momentum after an event – even if the collision is inelastic.