IN PROGRESS ⚙️ Mechanics

What is a scaler quantity?

Only direction

What is vector quantity?

Magnitude and direction

Example of scaler force?

Speed, mass, distance, temperature

Example of vector force?

Velocity, force, displacement, acceleration

What is momentum equation?

P=mv

What are three conditions of equilibrium?

1. All forces sum to 0/ resultant force is 0 (up=down)

2. $\Sigma$ of clockwise moments = $\Sigma$ anticlockwise moments around any point

How can equilibrium be shown with vector?

• Triangle of forces (tip-tail)

• Revolving horizontally & vertically forces and them adding to 0

What are moments defined as?

Force x perpendicular distance from the pivot to the line of action of the force

M = F x d

(Nm) = (N) x (m)

What is a force couple?

A pair of equal and opposite co planar forces

How to work out moment of force couple

F x d (between both forces)

What is the principal of moments?

For any object in equilibrium $\Sigma$ of clockwise moments = $\Sigma$ anticlockwise moments around any point

What is the centre of mass?

• A point where centre of mass can be considered to be concentrated

Where line of action of weight force acts from

The centre of mass in uniform solid objects is considered to be at centre of object

Where is the centre of mass in a solid uniform object?

At centre of objects

What is difference between displacement and distance?

Displacement is vector (straight line from point A to B)

Distance is scalar

What is equation of average speed?

$$Average.Speed=\frac{Total.Distance}{Total.Time}$$

What is equation of average velocity?

$$Average.Velocity=\frac{Total.Displacement}{Total.Time}$$

What is instantaneous velocity?

Velocity at a particular point in time

$V=\frac{\Delta s}{\Delta t}=\frac{ds}{dt}$

How to calculate instantaneous velocity?

Gradient of tangent in displacement/time graph

$V=\frac{\Delta s}{\Delta t}=\frac{ds}{dt}$

What is speed?

Rate of change of distance

Speed=distance/time

What is velocity?

Rate of change of displacement

$V=\frac{\Delta s}{\Delta t}=\frac{ds}{dt}$

What is acceleration?

Rate of change of velocity

$a=\frac{\Delta v}{\Delta t}=\frac{dv}{dt}$

What is area under velocity/time graph?

Displacement

$$\int vdt=s$$

In F=ma what does each letter represent

F= force

M= Inertial mass

A= acceleration

What suvat doesn’t include s?

$$v=u+at$$

What suvat doesn’t include t?

$$v^2=u^2+2as$$

What suvat doesn’t include v?

$$s=ut+\frac12at^2$$

What suvat doesn’t include a?

$$s=\frac12\left(u+v\right)t$$

What is gravity downwards?

9.81$ms^{-2}$

What is velocity at maximum height

v=0 (turning point)

What are 2 experiments to determine gravitational acceleration?

1. Manual timing

2. With a light gate

What is manual timing practical to determine gravitational acceleration?

Manual Timing

1. Drop a marble from different heights

2. Record time taken to reach ground

3. Measure height in h with ruler

4. Measure time t with stopwatch

5. Plot graph of h against t²

$$h=\frac12gt^2+0$$

$y=mx+c$ $m=\frac12g$

The gradient m is equal to a ½ g

What error with there be manual timing practical to determine gravitational acceleration?

Error & Uncertainty

• As uses human reaction time there will be error (time) and as t² the error will increase

How can error be reduced in manual timing practical to determine gravitational acceleration?

To reduce:

• Make the height as large as possible to reduce percentage uncertainty

• Additionally a trapdoor with an electromagnetic connected to timer can be used to reduce percentage error

What is Newtons 1st Law?

An object will stay at a state at rest or moving a constant velocity unless acted upon by a resultant force

What is Newtons 2nd Law?

For a constant mass: $F=ma$

• The net force of an object is proportional to the rate of change of momentum in the same direction

$$F=\frac{\Delta\rho}{\Delta t}$$

What is Newtons 3rd Law?

When a object A exerts a force on object B, object B exerts an equal and opposite force on object A

What is the name of two forces formed due to newtons 3rd law?

A newton pair

What makes something a newton pair (newton’s 3rd law applies)?

1. Forces must be on two different bodies

2. Forces must be of the same nature

What is an impulse?

The average net force acting on an object multiplied by the time it acts on it

$$F\Delta t=\Delta\rho$$

Impulse $=\Delta\rho$

$$=\rho_1-\rho_2$$

What is equation for impulse?

$$F\Delta t=\Delta\rho$$

Impulse $=\Delta\rho$

$=\rho_1-\rho_2$ $=\Delta\rho$

How to calculate impulse from force/time graph?

Area under graph is Impulse = change in momentum

How to estimate are under graph (3 ways)?

1. Rectangles

2. Counting squares: setting scale factor for each square

3. Integrating

What is unit of momentum?

$\rho=mv$ $\left(\operatorname{kg}ms^{-1}\right)$

What is definition of momentum?

The total momentum before a collision is equal to the total momentum after a collision, provided no external force acts on system

What is a perfectly plastic collision?

A collision where:

1. KE is fully conserved

2. Momentum is conserved

Generally in elastic collisions objects move away from (bounce off) each other.

What is real world example of perfectly elastic collision?

Molecular motion - particles perfect elasticity

What is a perfectly inelastic collision?

A collision where:

1. KE is NOT conserved

2. Momentum is conserved

Generally in inelastic collision the objects move together after collision at some velocity

What is conserved in elastic and inelastic collision?

Momentum

How is momentum conserved in 2d momentum problems?

$\rho$x before = $\rho$x after

$\rho$y before = $\rho$y after

• momentum is conserved independently in x and y axis

If a ball is travelling horizontally to the x axis and collides with another ball what is the momentum before collision in y direction?

0

How will a body move if there is NO resultant force applied to it?

At a constant velocity or remain stationary

How will a body move if there is a resultant force applied to it?

It will accelerate or decelerate

In Newtons 2nd law what is force proportional to?

Force is proportional to acceleration

Is acceleration always in same direction as resultant force?

Yes

What is free fall?

When gravity is the only thing acting on an object

Why do all objects in free fall accelerate at the same rate?

Due to gravity

What did Galileo do to test for free fall?

1. He set up an incline ramp (didn’t have technology to record time taken for object falling and reduces affect or air resistance)

2. Rolled a ball down it a different fractions of the length and discovered $distance$ is proportional to $\sqrt{time}$

3. So free fall objects accelerate at same rate

Why when doing a test using a distance would you use the largest length possible?

To reduce percentage uncertainty

What is percentage uncertainty?

$$\frac{absolute.uncertainty}{measured.value}\times100$$

Why do all objects fall at same rate (free fall)?

Mass = $m_1$

Acceleration = $a_1$

$$F=m_1a_1$$

As only force acting on object during free fall is gravity

$$W_1=m_1g$$

$$m_1g=m_1a_1$$

$$g_1=a$$

Therefore $a=9.81$ irrelevant of what the mass of the object is

What force does air resistance create?

Drag force - acts in opposite direction of motion

How does drag force affect velocity?

It will reduce the horizontal velocity and horizontal distance a projectile can travel while steeping the angle of descent