momentum is a **...** quantity

momentum is a **vector** quantity

what is the equation for momentum?

momentum (kgm/s) = mass (kg) x velocity (m/s)

M = m x v

rearrange the equation for momentum to make mass the subject

mass = momentum ÷ velocity

m = M ÷ v

rearrange the equation for momentum to make velocity the subject

velocity = momentum ÷ mass

v = M ÷ m

vector quantities have a **...** and a **...**

vector quantities have a **magnitude** and a **direction**

a car is moving at 15m/s in a northerly direction

it's mass is 2,000kg

calculate the momentum of the car

M = m x v

= 2000 x 15

= 30, 000 kgm/s north

what is the equation for velocity?

velocity (m/s) = distance (m) ÷ time (s)

v = d ÷ t

which direction does momentum act in?

in the direction of the velocity

explain the statement: the momentum of an object is directly proportional to its mass and velocity

M = m x v

as mass and velocity increase or decrease the momentum will increase or decrease proportionally (by the same factor, or by the same proportion)

what does proportionally mean in directly proportional?

by the same factor, or by the same proportion

calculate the momentum of an 80kg man running 10m/s

M = m x v

= 80 x 10

= 800 kgm/s

calculate the momentum of a 50g ball moving at 80km/h

M = m x v

convert 80km/hour into m/s so x 1000 ÷ (60 x 60) = 80000 ÷ 3600 = 22.2

convert 50g into kg so 50 ÷ 1000 = 0.05

= 0.05 x 2.2

= 1.1 kgm/s

a 1300kg car has the momentum of 3900kgm/s acting North

calculate the velocity of the car

M = m x v so v = M ÷ m

= 3900 ÷ 1300

= 3m/s North

a hammer is moving at 15m/s and has a momentum of 11.25kgm/s

calculate the mass of the hammer

m = M ÷ v

= 11.25 ÷ 15

= 0.75kg

what is the principle of the conservation of momentum?

the principle of the conservation of momentum states that the momentum is always conserved in a collision, provided there are no external forces (e.g. air resisitance, friction) acting on the system

give two examples about external forces that could disrupt the principle of the conservation of momentum

air resistance

friction

how does this illustrate the conservation of energy?

Before, the velocity is zero. Therefore, the momntum of the dynamte is zero as M = m x v. After, the dynamite explodes in the exact opposite direction (positive and negative). The equal positive and negative momentum cancel each other out having a total momentum of zero. This proves the conservation of momentum as the total momentum before must, and does, equal the total momentum after.

A ball which has 5kg mass and is moving east at 10m/s which knocks into another stationairy ball with the mass of 5kg.

Calculate the momentum before and after and calculte the velocity of the balls after

total momentum before = total momentum after

MaVa + MbVb = (Ma +Mb)V

(5 x 10) + (5 x 0) = (5 +5)V

50kgm/s = 50 ÷ (10) = V

5m/s = V

A ball which has 5kg mass and is moving east at 10m/s which collides with another ball with the mass of 5kg moving 5m/s west.

Calculate the momentum before and after and then calculat the velocity after

CHECK THE SHEET FOR THIS

total momentum before = total momentum after

MaVa - (backwards direction) MbVb = MaVa + MbVb

(5 x10) - (5x5) = (5 x 2) + (5 x V)

25kgm/s = 10 + (5 x V)

5 x 3 = 15, + 10 = 25

V = 3m/s

how do you convert milliseconds into seconds?

÷ 1000

how do you convert millimetres into metres?

÷ 1000

Use the conservation of momentum to calculate the recoil velocity of the gun:

mass of gun = 1.00kg

mass of bullet = 0.05kg

before: gun and bullet stationairy

after: gun recoils backwards, bullet moves fowards (east) at 300m/s

MgunVgun + MbulletVbullet = MgunVgun + MbulletVbullet

(1.00 x 0) + (0.05 x 0) = (1.00 x ?) + (0.05 x 300)

0 + 0 = (1.00 x ?) + 15

after momentum must equal to 0 as before momentum equals 0

15 ÷ 1.00 = 15

therefore, recoil velocity of the gun = 15 m/s backwards (west)

The recoil velocity of a 1.00kg gun is 15 m/s backwards (west)

Explain what would hapen to the recoil velocity if the gun was held by a 99kg person?

the velocity would decrease to x100 smaller as the mass of the gun is now 100kg (1.00kg + 99kg)

the recoil velocity is now 0.15m/s

What equation connects force, change in momentum and time taken for change to happen?

force acting (N) = change in momentum (kg m/s) ÷ time taken for change to happen (s)

What is Newton's third law?

if object A exerts a force on object B then object B exerts the excat opposite force on object A

every action has an equal and opposite reaction

What does "every action has an equal and opposite reaction" mean?

The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second objec

Newtons Second Law (F = ma) to explain how safety features reduce the impact focus in a car crash?

seatbelts, airbags and a cripple zone increase the time taken for a change in momentum so that the impact force decreases

you cannot reduce the change in momentum - it is fixed

the only way to make the force smaller is to make the time bigger as this is an inverse equation

N.B. all always quote and reference this equation

What is Newton's second law?

impact force = (final momentum - initial momentum) ÷ time for change

F = (mv - mu) ÷ t

F = m(v-u) ÷ t

(v-u) ÷ t = acceleration

F = ma

force = mass x acceleration