TRIPLE CONTENT: Momentum + moment

Formula for momentum + unit

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

Important info about momentum

An object at rest does NOT have momentum/has 0
Momentum can be positive or negative.
Momentum keeps an object moving in the same direction. It is difficult to change the direction of an object with a large momentum.

When does the momentum of an object change?

• Velocity increases or decreases (acceleration)
• Direction changes (acceleration)
• Its mass changes

What is the conservation of momentum?

It states that the total momentum before an interaction (collision or explosion) is equal to the total momentum after an interaction, if no external forces are acting in the objects.

Explotion calculation:
A cannon ball of mass 4.0kg is fired from a stationary 96kg cannon at 120m/s. Calculate the velocity (V) of the cannon immediately after firing.

p = mv

Total momentum before = total momentum after
0 (neither object is moving at first) = 0 (because momentum is conserved)

Momentum of cannon after + momentum of ball after = 0
[m(ball) x v(ball)] + [m(cannon) x v(cannon)] = 0
(4.0 x 120) + (96 x V) = 0
480 + (96 x V) = 0
96 x V = -480
V = -480/96
= -5.0 m/s

Note that it is negative because cannon is moving backwards.

Sticky collision calculation:
Train wagon A is moving towards a stationary train wagon B at a velocity of 3m/s. Wagon A weighs 2kg and wagon B 8kg. Both wagons link together and continue moving forward together. Calculate the velocity of the wagons after they link.

p = mv
u = initial velocity. v = final velocity. p = momentum

Total momentum before = total momentum after
Initial p of wagon A + Initial p of wagon B = momentum of both after
[m(A) x u(A)] + [m(B) x u(B)] = m(A+B) x v(A+V)
(2 x 3) + (8 x 0) = (2 + 8) x v(A+B)
6 + 0 = 10 x v(A+B)
v(A+B) = 6/10
= 0.6 m/s

REMEMBER that for this one p after p of them COMBINED so it is NOT (mass of A+B) + (velocity of A+ B) but (mass of A+B)(velocity of A+B)

What momentum will have 2 identical objects moving in opposite directions (e.g towards each other) at the same speed?

Since momentum is a vector there will be no momentum as they will cancel each other. Momentum is always conserved over time.

Formula for force 2.0

change in momentum
Force = ——————————————-
time

∆p (mv-mu)
F = ——— OR —————-
t t

What safety measures are used to prevent injuries in vehicles, gymnasiums, playgrounds, bicycles?

• Seatbelts, airbags, crumple zones.
• Crash mats
• Bicycle helmets

Using the ideas of momentum and force, explain why car crashes can cause injury to the passengers

F = change in momentum/time

When there is a car crash, the car and the passengers decelerate rapidly.
They experience large forces because of the very fast change in momentum - and these large forces can cause injuries.

Using ideas of momentum and force, explain how a seat belt reduces the risk of serious injury in a car crash. (4)

F = change in momentum/time (not a mark but por si las moscas)

• During collision, seatbelt stretches.
• Even though there is same momentum change (with or without seatbelt)
• time of impact increases
• which reduces the RATE of momentum CHANGE (it does not reduce momentum) .
• therefore reducing the average force.

How about cushion surfaces (e.g crash mats) or crumple zones?

• Thick and soft (to offer shock absorption or the force created by the person landing).

• Even though same momentum change

• This increases the contact time so the rate of momentum change decreases.

• Results in smaller impact force

• Crumple zones increase the time over which the VEHICLE comes to rest, lowering the impact force on the passengers (ya después añades todos los key things del resto)

For FEB 2025 exam:
What is Newton's third law? How can you recognise this in a diagram?

Whenever 2 objects interact, the forces they exert on each other are equal (in magnitude) and opposite (in direction).

1. The two forces act on different objects
2. The two forces always are equal in magnitude but act in opposite directions
3. The two forces are always the same type: weight, reaction force, etc

Newton's third law in explosions.
A man (60kg) is pushing a box (120kg) with 100N of force. Describe and explain what will happen.

• The object will also push back with 100N of force (normal contact force).
• The man will be moving backwards more as its mass is smaller than the box's.
• This is because of Newton's second law (F=ma). While the forces are equal and opposite, the acceleration will not be equal as it also depends on the mass.

For objects with equal mass, they will have equal accelerations.
For objects of unequal mass, they will have unequal accelerations.

What is a moment? Formula

The turning effect of a force exerted on an object about a pivot.

Moment (Nm/Ncm) = force (N) x Perpendicular distance from the pivot (cm or m)
M = F x d
If no asked unit for distance always convert to metre

Two spanners with different lengths are screwing a screw. Which one will require a bigger force and why?
—————-( ———-(
12cm 5cm

The smaller one because m=Fxd so a bigger distance (length of spanner) to the pivot would result in a bigger moment. So less force is needed to result in the same moment.

Where is the pivot?

It is the point where the surface is going to rotate

What is the principle of moments?

For an object in equilibrium the sum of the clockwise moments is equal to the sum of the anticlockwise moments about the same pivot.

NOTE: moments are clockwise or anti-clockwise.

What happens if distance is 0?

There is no turning effect (force is in line with pivot)

| ↗ |
| l | <~ SPANNER. @ is the screw, which is the pivot
[ @ ].
l <~ distance

In this diagram object € weighs 60N and its distance from the pivot is 5m; £ weighs 15N and its d from the pivot is 2m; ¥ weighs 27N and its d from the pivot is 10m. They are on a see-saw.
Will the beam rotate clockwise, anti-clockwise or stay balanced?

€ £ ¥
—————————————-
| <~ pivot

Sum of anti-clockwise moment.
M(€) = 60 x 5
= 300Nm

Sum of clockwise moment
M(£ + ¥) = (15 x 2) + (27 x 10)
= 30 + 270
= 300Nm

The see-saw will stay balanced/in equilibrium.

Supporting a beam.
A light beam is one that can be treated as though it has no mass.
Therefore the supports must exert upward forces that balance the downward acting weight of any object placed on top of the beam. These supports act as 2 pivots

Force 2 _ Force 1 ↖ ||| ↗ --|—————|———--|-— | |. ^ | | || Weight |__|

What will happen in terms of forces if the object in the above diagram is moved to the right hand side?

What about if we remove Force 2 support?

Force 1 will decrease and Force 2 will increase.

Force 2 would be 0. The weight of the object would produce a moment about the left hand support causing the bean to pivot clockwise.

Why does the force have to be bigger?

Because of the principle of moments:

Moment = distance x force.

The principle of moments states that for an object in equilibrium, the sum of the clockwise moment must be equal to the sum of the anticlockwise moment.
When the object is closer to support A (force 2), the distance between the object and the support is smaller, so the support needs to exert a bigger force to equal the anticlockwise moment created by the object's weight.

REMEMBER THAT BOTH SUPPORTS ACT AS PIVOTS (isolate them, imagine there is only one pivot and work out the moment for that). So no lo entiendes mira el vídeo de yt "moments with two pivots"

Where does the weight of a body act?

Through its centre of gravity

How can we work out the center of gravity on an drawn object (if it is not given)?

By drawing lines of symmetry so the point where these lines intersect is where the center of gravity is.

Diagrams in the cuaderno explain it much better (DONT BE LAZY AND TAKE A DAMN LOOKIKK).
In a diagram how will we know if the object will return to an equilibrium?

If the line of action (where weight is acting downwards) does not go past the base of the object/the pivot, the object will tilt back to equilibrium.

What is a stable object? What characteristics will these object have?

An object that if disturbed slightly from equilibrium point it will return back to equilibrium.
Large base.