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## 2020-05-25

### Application for the principles of momentum conservation

1.       Billiard / Pool game

Billiards game uses a ball to hit other balls into holes. The more momentum the cue ball has the greater the momentum force exerted on the target ball / balls.

2.       Water hose

Water that jets out from a firemen hose exerts high backward force, hence firemen needs to hold fast the hose to prevent it from moving.

3.       Boat

When rowing a boat, the backward force exerted by the rower will result in the same forward force being produced.

4.       Jet engine

The hot gas and vapour ejected at the exhaust of a jet engine will produce an upward and forward force, equal to the force exerted by the hot gas.

5.       Rocket

A mixture of oxygen and hydrogen are burned up in the combustion chamber. This creates a very high pressure and force which is expelled at the bottom of the rocket. As a result, an upward force of similar magnitude is produced.

## 2020-05-15

### Linear momentum collision problem calculations 2

Questions

1.     A toy truck with a mass of 3 kg was moving at 3 ms-1 and hit with another toy truck of 1 kg and was moving with a velocity of 1 ms-1, in the opposite direction. After collision, both trucks moved together in the same direction, calculate the common velocity of the two objects after collision.

m1u1 + m2u2 =  (m1+ m2)v

(3)(3) + (1)(-1) = (3+1)v

9 – 1 = 4v

v = 2 ms-1

2.     A hunter shot a 100g bullet from a 1.5kg gun. If the bullet travelled 200 ms-1 after being triggered, what is the backward jerk of the gun. (Think final backward velocity of the gun).

Total initial momentum = Total final momentum = 0

m1u1 + m2u2 = 0

1.5(v) + 0.1(200) = 0 ß make sure to convert 100g to kg

1.5v +20 = 0

v = - 13.3 ms-1   ß Value is negative because gun moved in opposite direction

3.     A trolley of mass 2 kg was in a stationary condition, before a 5 g sticky plasticine was thrown into it with a velocity of 500 ms-1. After hitting the trolley, the plasticine sticks into it. Calculate the final velocity of both the trolley and plasticine?

Use the classic formula of momentum conservation

m1u1 + m2u2 = m1v1 + m2v2

0.005 (500) + 2 (0) = (0.005+ 2)v

2.5 = 2.005v

v = 1.245 ms-1

## 2020-05-03

### Linear momentum calculation 1 (Collisions)

The principle of conservation of momentum:

Total momentum before collision = Total momentum after collision

Inelastic collision

1. An object of mass = 2 kg with initial velocity of  30 m/s hit a stationary object of mass = 4 kg. After the collision, both objects move together with identical velocity. Calculate the final velocity of both objects.

Total momentum before collision

= m1u1 + m2u2
= 2(30) + 4 (0)
= 60 kg ms-1

Total momentum after collision = 60 kg ms-1

= m1v1 + m2v2
= 2v + 4v
= 6v

Remember
60 kg ms-1 = 6 v

Final velocity for both objects, v = 10 ms-1

Elastic collision

1. An object of mass (object 1) = 2 kg with initial velocity of  40 m/s hit an object of mass (object 2) =3 kg with initial velocity = 20 m/s. After the collision, object 1 moves with v= 30 m/s. Calculate the final velocity for object 2.

Total momentum before collision
= m1u1 + m2u2
= 2 x 40 + 4 x 20
= 160 kg ms-1

Total momentum after collision
= m1v1 + m2v2
= 2 x 30 + 4 v2
= 60 + 4 v2

Final velocity of object 2

160 = 60 + 4 v2
4 v2 = 100

v2 = 25 ms-1

3. Object 1 (m1 = 2 kg) moves with  initial velocity (u1= 20 m/s) and hits object 2 (m2 = 1 kg) (u2 = - 5 m/s) which moves in the opposite direction. After the collision, Object 1 moves with velocity = 15 m/s. Calculate the velocity for object 2, assuming that the collision is elastic.

Total momentum before collision

= 2 x 20 + 1 x (-5) negative denotes opposite direction
= 35 kg ms-1

Total momentum after collision
= 2 x 15 + 1 x v2
= 30 + v2

Final velocity of object 2, moving in the same direction
35 = 30 + v2

v2 =  5 m/s