P8: Forces in balance

Scalar quantity

Only have magnitude (size)

6 examples of scalar quantities

1. Mass

2. Temperature

3. Speed

4. Energy

5. Distance

6. Time

Vector quantity

Have magnitude and direction

6 vector quantity examples

1. Displacement

2. Weight

3. Force

4. Velocity

5. Acceleration

6. Momentum

Is displacement vector or scalar?

Vector

• Distance given direction

• Eg 500 m (magnitude) due west (direction)

How do you represent vectors?

Arrows

• Length of arrow = magnitude of vector

• Direction of arrow = direction of vector

Is force a vector or scalar quantity?

Vector

• F = m x a

• Size + direction

How do you represent forces on an object when more than 1 force acts on the object?

Scale diagram

• 1 unit of distance represents a force of 1N

• 30 mm arrow and 40 mm arrow

Vector quantities of distance, speed and mass

1. Distance, displacement

2. Speed, velocity

3. Mass, weight

Force

A push or pull that acts on an object due to the interaction with another object

• Vector, N

Contact forces

Force that acts between objects that are physically touching

Example of contact forces

1. Friction

2. Air resistance

3. Tension

4. Normal contact force

Example of how air resistance is a contact force- use example of a skydiver

1. As they fall through the air, air particles collide with the parachute

2. Causes force of AR to act upwards

Normal contact force/reaction force

An object at rest on a surface exerts a force on the surface

• Reaction force acts at right angles to the surface

Non-contact forces

A force that acts at a distance when objects are physically separated

Examples of non-contact forces

1. Gravitational force- attracts all objects to other objects

2. Electrostatic force- betw 2 charged objects (attraction/repulsion)

3. Magnetic force- experienced by certain objects in a magnetic field

Effects a force can have on a body

Can change their:

1. Speed

2. Direction

3. Shape

Newton’s 3rd law of motion

When 2 objects interact with each other, they exert equal + opposite forces on each other

When a car moves forward:

The force of friction of the…

1. Road on the tyre = in the forward direction

2. Tyre on the road = in the reverse direction

Force equation

force (N) = mass (kg) × acceleration (m/s²)

Resultant force

A single force that has the same effect as all forces acting on the object

Altitude

Height above ground

Newton’s first law of motion

When forces acting on an object are balanced….

Resultant force on object = 0

If the object is:

• At rest → it stays stationary

• Moving → keeps moving w same speed + direction

Free body scale diagram of an aeroplane flying at a constant altitude at a constant velocity

• Up + down arrows same length = balanced = constant altitude

• Front + back arrows same length = balanced = constant velocity

If 2 forces acting on an object have a 0 resultant force then the forces must be…

Equal + act in opposite directions to each other

What happens when forces acting on an object are unbalanced?

(resultant force isn’t 0)

An object will

• change speed (accelerate or decelerate)

• or change direction

When an object is acted on by 2 unequal forces acting in opposite directions, the resultant force is…

• Equal to the difference between the 2 forces

• In the direction of the larger force

Free-body force diagram of an object

Shows all the forces acting on 1 object

• Object = dot

• Forces = arrow

Moment of a force

The turning effect of a force about a pivot

What does the moment of a force measure

The turning effect of a force on an object

Moment (Nm) of a force equation

Force (N) x distance (d) = Moment (Nm)

• M=fd

Distance when calculating the moment of a force

d must be perpendicular from the line of action of the force to the pivot

How can you increase the turning effect (moment) of a force?

• Increase size of the force (F)

• Increase d- use a spanner with a longer handle

Load

Weight of the object

Effort

Force the person applies to the crobar

Line that a force acts along

Line of action

Why levers are force multipliers?

Can exert a force greater than the effort

• Effort can move a greater load

Pivot

Point of rotation

Examples of levers

• Hammer- to remove a nail

• Crowbar- to lift a plank of wood

What does a lever allow us to do?

Lift a heavy object by applying a small amount of force

What can levers and gears do?

Transmit the turning effects of forces

What do gears do if:

• gear A is connected to the turning force of the engine

• + gear B is connected to the wheels?

Transmits the turning force from the engine to the wheels

Describe the turning effect of these 2 gears and why

• gB = 2x the radius of gA

• TE of gB = 2x as large as gA

• gA rotates 2x everytime gB rotates 1

• So WD by 2 gears = same

How do gears work?

1. 1 gear turns → the other must also turn

2. Gears meet → teeth will move in the same direction (e.g. downwards)

3. Then 1 gear will move move clockwise, + the other anticlockwise (in opposite directions)

What does the moment (TE) produced by a gear depend on if the force applied to both is the same?

Size of the gear

• radius of the gear (from pivot)

Why does the moment produced by a gear depend on its size?

TF on the larger gear acts further from its pivot than the TF of the smaller gear wheel acting on its pivot

• M = Fd

What happens when a low gear is chosen?

• Small gear turns large gear

• Large gear turns slower

• TE of large gear > small

What happens when a high gear is chosen?

• Large gear turns small gear

• Small gear turns faster

• TE of small gear < large

Low gear vs high gear

1. L- Low speed, high TE

2. H- High speed, low TE

When an object is balanced…

Total clockwise moment about a pivot = total AC moment about that pivot

• AC x m = C x m

What do gears do?

Change the moment of a turning effect

How can gears increase the moment of a turning effect (give a bigger TE)

Small gear must drive a large gear wheel

Gravity

Force of attraction between objects

• Non-contact force

• Vector

Mass

How much matter is in an object

• Scalar

• kg

• Doesn’t depend where an object is

Weight

Force acting on an object due to gravity

• Newton

Gravitational field strength (g)

A measure of the force of gravity in a particular location

Weight equation

Mass (kg) x g (N/kg) = Weight (N)

Relationship between weight and mass of an object

Weight of an object directly proportional to its mass

• Weight ∝ Mass

• Double mass = double weight

How can you measure an objects weight?

Newton meter or calibrated spring balance

Centre of mass

The single point through which the weight of an object acts

Where is the centre of mass of a uniform ruler?

Its midpoint

Suspension in equilibrium:

What happens when you suspend an object and then release it?

1. Comes to rest (equilibrium) with its CoM directly below the point of suspension

2. Its weight doesn’t exert a TE on the object → as its CoM is directly below the point of suspension

Suspension in non-equilibrium:

What happens when you turn an object from its equilibrium position?

• Returns back to its equilibrium position

• As its weight has a TE that returns an object to equilibrium

What does it mean if an object is freely suspended?

It returns to its equilibrium position after the turning force is taken away

Where is the centre of mass of a symmetrical object?

Along the axis of symmetry

• More than 1 axis of symmetry → where they meet

Balanced moments

Clockwise moment = anticlockwise moment

• W1d1=W2d2

What happens when moments are balanced

Resultant moment is 0

• Object does not move or turn

Principle of moments

If an object is balanced:

Total C moment about a pivot = total AC moment about that pivot

Forces that can turn an object at a fixed point

All forces acting on an object that don’t pass through a fixed point

How do you know if a turning force will turn an object clockwise or anticlockwise

Depends on the

• Direction of the force

• Position of the fixed point

Why do objects remain stationary?

Use the example of a block on a flat surface

Weight of the block acts directly down from the CoM

Why do objects topple?

• Tilt the block → line of action of the weight is outside the base of the object

• → resultant unbalanced moment acting on the block

Conditions for an object to be in equilibrium

• Resultant force on it is 0

• Forces acting on the object have no overall turning effect

What does the weight of an object depend on?

The GFS at the point where the object is

What can a single force be resolved into?

2 forces acting at right angles to eachother

• The 2 component forces tog have the same effect as the single force

If the resultant force is 0, what happens if an object is

1. At rest

2. Moving

1. Remains stationary

2. Keeps moving in the same direction + speed

If 2 forces act on an object along the same line, the resultant force is:

1. Sum- if Fs act in same direction

2. Difference- if Fs act in opposite direction

When is work done on an object?

When a force causes an object to move thru a distance

A force does work on an object when…

The force causes a displacement of the object

1 J of work done =

1 N force causes displacement of 1m

How do frictional forces lead to an increase in temp?

WD against FF acting on an object cause a rise in the temp of the object

What can cause an object to rotate?

Force / system of forces

If an object is balanced (in relation to moments)

Total C moment about a pivot = total AC moment about the pivot

A lever used as a force multiplier…

Exerts a greater force than the force applied to the lever by the effort

What are gears used to do?

Change the moment of a turning effect

How is a lever a force multiplier

Force applied to lever is further away from pivot + smaller in size than the force the lever applies on the object

If someone sits at the centre of a seesaw, why is the moment about the pivot 0?

Weight of the person acts downwards thru the pivot