MOVING ABOUTFocus 4: Momentum and Force

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 = mv

and 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

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 byp = mv

p = momentum measured in kgms-1

m = mass measured in kg v = velocity measured in ms-1

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.

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 – muUsually the mass of an object remains the same therefore

p = m(v – u) I = Ft

So Ft = m(v –u)

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 = maThis is how Newton actually got to his second law.

t

uvmFnet

)(

t

uv )(

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.