a2 h 41a momentum

8/12/2019 a2 h 41a Momentum

1/17

Momentum, p

momentum = mass x velocityp = mv

min kilograms (kg)vin metres per second (ms-1)

pin kilograms metres per second (kg ms-1)

Momentum is a VECTOR quantity

direction the same as the velocity


2/17

Newtons 2ndlaw (A2 vers ion )

The resultant force acting on an object is

proportional to the rate of change of

momentum of the object and is in the same

direction as the resultant force.

F (p)

(t)


3/17

Inserting a constant of proportionality k

F = k(p)

(t)

but: p = mv

hence: F = k(mv)

(t)

If the mass, m remains constant:

F = km (v)(t)


4/17

but: (v) = a (acceleration)

(t)

hence: F = km aA force of one newton is defined as that required tocause an acceleration of 1 ms -2with a mass of 1 kg.

Inserting these values into: F = km a

gives: 1 = kx 1 x 1

and so: k= 1

giving: F = m a (the AS version of Newtons 2ndlaw)

Note: This simplified version only applies for an objectof constant mass.


5/17

Force and Momentum

Force is equal to the rate of change of

momentum.

F =(mv) /t

F in newtons (N)(mv) in kilograms metres per second (kg ms-1)

t in seconds (s)


6/17

Question 1

A car of mass 800 kgmoving at a velocity of30 ms -1is brought torest by a braking forceof 1200 N.

Calculate:(a) its initial momentum

(b) the time taken tostop the car.


7/17

Question 2

A car of mass 750kg

travelling at a speed of4.0ms -1is struck frombehind by another vehicle.The impact lasts for 0.30sand causes the speed of thecar to increase to 6.0ms -1.

Calculate:(a) the change inmomentum of the car due tothe impact.

(b) the impact force.


8/17

Impulse,p

Impulse is equal to the change ofmomentum produced by a force over aperiod of time.

Impulse, p = Ft

= (mv)

pis measured in newton seconds (Ns)


9/17

Forcetime graphs(Breithaupt page 6)

Impulse is

equal to the

area under aforce-time

graph.


10/17


11/17

Graph Question

Calculate the impulse andchange in velocity caused tomass of 6kg from the graphopposite.

2 5 t/ s

3.0

F / N


12/17


13/17

Question

A trolley of mass 4kg moving at 5ms-1collides with another initially stationary trolley

of mass 3kg. If after the collision the trolleys

move off attached together calculate theircommon final velocity.


14/17

Elastic and inelastic collisions

ELASTIC KINETICenergy is conserved

INELASTIC

Some (or all) KINETICenergyis transformed into thermal or other forms of

energy.

In both types of collision both the total

energy and momentum are conserved.


15/17

Collision question continued

Was the co l l is ion in the previous exampleelast ic o r inelast ic?


16/17

Explosions

KINETICenergy isincreased

Both the totalenergy andmomentum areconserved


17/17

Question

A gun o f mass 3kg f ires a bul let of mass15g . If the bu l let moves o ff at a speed o f

250ms-1calcu late the reco i l speed o f the

gun.

a2 h 41a momentum

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