Chapter 4: Forces in action

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Mass

Is a property and is measured in kg

Resists change in motion

Greater the mass of a body, the smaller the change produced by an applied force

Definition of mass

Measure of an amount of matter in an object

Weight

As it is a force on an object due to the pull on gravity,

its measured in Newtons (N)

The weight is equal to:

w = mg

g: changes depending on the planet

Definition of weight

Effect of a gravitational field on mass

Free fall

- it is solely falling under the influence of gravity

- on Earth every object accelerates at 9.81 ms^-2

- in the absence of air resistance - all bodies near the

Earth fall with the same acceleration- regardless of their

mass

Force and acceleration

according to newtons second law, objects will accelerate if

there is a resultant force exerted on them

this acceleration is in the same direction as the

resultant force

F = ma

RESULTANT FORCE

force is directly proportional to acceleration (when mass is

constant)

Geometric centre

The middle of an object

Centre of mass and geometric centre

Objects with uniform density - the centre of mass is

the geometric centre of the object

A force being applied at the objects centre of mass will

produce a straight line motion without rotation.

Weight (centre of gravity)

W = mg

Weight (W) - the resultant gravitational force, will act

through the point - centre of gravity (which coincides with

the objects centre of mass)

Finding the centre of gravity

A freely suspended object will come

to rest with its centre of gravity

below the the point the object is

suspended by.

It produces a vertical line which

is inline with g and the centre of mass

Centre of gravity of another object

Free-body diagram rules

• draw each vector head to tail

• anchor the vectors from the centre of mass

• label each vector arrow

• the length of the arrow represents the size of the force

Different forces

• weight

• friction

• drag

• upthrust

• thrust

• tension

• normal contact force !!

Weight (force)

gravitational force produced when a mass in a

gravitational field (g)

• acts through the objects centre of mass

ALWAYS DRAWN STRAIGHT DOWN

Friction

opposes motion of an object

Drag

opposes motion when an object is travelling through a fluid

(gas / liquid)

because the object collides with particles in the fluid

Upthrust

an upward buoyancy force acting on an object when it is a

fluid. this is due to the pressure difference between the top

and bottom of a submerged object

Tension

the force within a stretched cable / rope

Normal contact force

when an object rests

against another (is

stationary).

the normal is at 90 degrees where the objects touch

Compare the force drag and the force friction

- both forces oppose the motion of an object

- drag is when an objects motion is opposed by a fluid (liquid or

gas)

- while friction is when an objects motion is opposed by its

surface being in contact with another object

Factors affecting drag

- ↑ cross-sectional area ↑ drag

- ↑ speed ↑ drag

Relationship between drag and speed

drag ∝ speed²

Terminal velocity

As the speed of an object increases, the drag does.

This continues until the drag force balances the weight of the

object.

It has now reached terminal velocity.

Turning moments

• the turning effect of a force and can be

  clockwise / anti-clockwise

can occur when forces cause objects to rotate at a point

Moment definition and formula (Nm)

force x perpendicular distance of the line of action of force from

the axis / point of rotation

= Fx

Force (N)

Perpendicular distance (m)

Force applied at an angle (Moments)

Equilibrium: principle of moments

When a body is in equilibrium, the net forces and the net moments on an object is zero.

• the object is not accelerating - no net forces

• the object is not rotating - no net moment

no net moment means clockwise moment = anti-clockwise moment

Translational motion

object moving through space

Making an object move with no translational motion

Apply equal and opposite forces

Couples

Forces that produce rotational motion and no translational

motion

the moment of a couple doesn’t depend on a povot, only the

perpendicular distance between the two forces

A couple consists of two forces that are..

• equal in magnitude

• opposite in direction

• perpendicular to the distance between them

• couples produce a zero resultant force - the object doesn’t accelerate

• the size of the turning effect is given by the torque

Torque of a couple (Nm)

one of the forces (N) x perpendicular sperating between the forces (m)

Equilibrium

A system is in equilibrium when all the forces are balanced:

• no resultant force

• no resultant torque

An object as equilibrium will therefore remain at rest / constant

velocity - DOESN’T ROTATE

Coplanar forces in equilibrium

can be represented by vector triangles.

In equilibrium - they’re closed triangles - form a closed path

Triangular forces in equilibrium