# AS Physics 1

Revision cards for Edexcel Physics unit 1 - Mechanics and materials

- Created by: Tara Wheeler
- Created on: 08-05-09 09:38

## Scalar and Vectors

**Scalars** only have **size**, **Vectors** have **size and direction**.

- Scalars - mass, temp., time, length, speed, energy.
- Vectors - displacement, force, velocity, acceleration, momentum.

You can **add vectors** using **pythagoras** (a2 + b2 = c2) and **trigonometry** (SOHCAHTOA). You can also use pythagoras and trigonometry for adding **resultant forces or** **velocities**.

When adding vectors make sure they are **tip to tail**, and if the vectors aren't at right angles you should do a scale drawing.

## Equations of Motion

**Uniform acceleration** is **constant** acceleration. Acceleration could mean a **change in speed** or **direction** of both.

The four **equations of motion** -

**V = u + at**

V is final velocity, u is intial velocity, a is accleration, t is time

**s = ut + 1/2 at^2**

s is displacement

**v^2 = u^2 +2as**

**s = (u+v)/2 x t**

## Newton's Laws of Motion

**Newton's 1st Law** - The velocity of an object will not **change** unless a **resultant force acts on it**. Eg. Apple on a table wont go anywhere because the forces on it are balanced.

**Reaction (R) = weight (kg)**

**Newton's 2nd Law** - **Acceleration** is **proportional** to the **force.**

**resultant force (N) =** **mass (kg) x acceleration (ms-2) [F = m x a]**

**Remember** - Resultant force is the vector sum of all the forces. The **acceleration** is **independant** of the mass.

All objects fall at **the same rate** (if you ignore air resistance).

**Newton's 3rd Law** - Each force has an **equal, opposite reaction force**. Eg. If an object A exerts a force on object B, then object B exerts an equal but opposite force on object A. The forces are always the same type but the forces are not both applied to the same object.

## Weight, Mass and the Centre of Gravity

**W = mg**

**Weight = mass x gravity**

Mass is **scalar** and force (weight) is a **vector**.

**Density** is mass per unit volume. Density **doesnt** vary with size or shape. Is it calculated by **p = m/v**

**Density = mass/ volume** (density is measured in **gcm-3** or **kgm-3**)

**Centre of gravity** - assume all the mass is in one place. An object will be nice and **stable** if it has a **low centre of gravity** and a **wide base area**.

## Forces

**Free body force diagrams** show all the **forces** on a **single body**. If a body is in **equilibrium** the forces acting on it will be **balanced**. Some of the forces to look out for - **mg (weight), drag, push, friction, resistance (to earth)**.

Force calculations - **Resolving a force**. Resolving a force means **spliting it into components - vertical and horizontal**. Replace the Force (F) with vertical force (Fv) and horizontal force (Fh) and this is resolving the Force (F). You use **trigonometry** to find **Fv** and **Fh**.

**Fh = F cos (the angle)**

**Fv = F sin (the angle)**

Use **vector addition** to get the **resultant force**. First add the vectors together and use **pythagoras** to get the length, then divide your A and B from pythagoras section, take that answer and put it to**tan-1**. You now have the angle, most answers go along the lines of **Force 999N at an angle 99 degrees from north**.

## Work

**Work** is done whenever **energy is transferred**.

**Work (J) = Force (N) x Distance (m) [W=Fs]**

**Work** is the energy thats been **changed** from **one form to another** - not always the total energy. The equation **assumes** that the direction of force is the same as the direction of movement.

**Definition of a Joule** - **one joule** is the **work done** when a force of **1 newton** moves an object through a distance of **1 metre**.

The direction of force isnt always in the same direction as the movement. If not you use **horizontal and vertical components**.

**W = Fs cos (the angle)**

## Power

**Power** equals **work done** **per second.**

**Power (W) = Work Done (J) / Time (s) [P=Wt]**

The **watt** is defined as a **rate of energy** transfer equal to **1 joule per second**.

**Power (W) = Force (N) x Velocity (ms-1) [P=Fv]**

This equation can be helpful when you are given **speed** in a question.Sometimes in a power question the **force** and the **motion** are in **different directions**, like with work, we then use **horizontal and vertical components**.

**P = Fv cos (the angle)**

## Mechanics in the Real World

Many **factors** affect how **quickly a car stops**.

**Thinking distance + Braking distance = stopping distance**

**Thinking distance = Speed x Reaction time**

Car **safety features** are usually designed to **slow you down** more gradually and increase the **collision time**, some are designed to **reduce the force** on you. Example features - **Seatbelts, airbags, crumple zones (at the front and back of the car) and safety cages** **(around the car to prevent crushing)**.

**Forces** act on **sports people**. People who bungee and rock climb have forces acting on them all the time, these can be shown using **free body diagrams** (see forces). **Gravity** is the **only** force acting on **projectiles**.

## Conservation of Energy

**Principle of Conservation of Energy** - Energy cannot be **created or destroyed**. Energy can be **transferred** from one form to another but the **total amount** of energy in a closed system will **not change**.

**Ek = 1/2 mv2** - **Kinetic Energy**

(m = mass, v = velocity)

**Eg = mgh** - **Gravitational Potential Energy**

(m = mass, g = gravity, h = height)

**E = 1/2 Ke2** - **Elastic Potential**

(e = extension, K= stiffness)

## Hookes Law

**Hookes law** states that **extension** is **proportional to force**.

**F = Ke** **(K = stiffness constant, e = extension)**

Hookes law can apply to **springs**. The **extension** or **compression** of a spring is proportional to the force applied. **Tensile** - stretch spring, **Compressive** - squash spring.

**Hookes law stops working** when the **load** is great enough. On a graph, if there is a **straight line relationship** between load and extension then **Hookes law is obeyed**.

When the graph starts to **curve**, this is where point E, the **Elastic limit** is. Increase the load past the elastic limit and the material will be **permanently strecthed**.

A strecth can be **plastic** or **elastic** -

**Elastic**- Material returns to its**original shape**when the forces are removed. For a metal, elastic deformation happens as long as Hookes law is obeyed.**Plastic**- Material is**permanently stretched**. A metal stretched past its elastic limit shows plastic deformation.

## Young Modulus

The **Young Modulus** is **stress/strain**. Below the limit of proportionality for a material, stress divided by strain is a **constant**, the constant is called the **Young Modulus (E)**. It is used by **engineers** to make sure materials can withstand forces.

**E = stress/strain = F/A / e/l**

To find the Young Modulus you need a **very long wire**. Use a rule, marker and a pulley with some weights. The **longer and thinner** the wire, the more it extends for the same force. Take the correct measurements down and you can find the Young Modulus.

Use a **stress-strain graph** to find **E**.

**Gradient = stress / strain = E (Young Modulus)**

The **area under** a stress-strain graph gives the **stored energy**. When **Hookes law** is obeyed the stress-strain graph will have a **straight line** so you can calculate the **energy per unit volume** -

**energy = 1/2 x strain x stress**

## Stress and Strain

A **stress** causes a **strain**.

**Stress = F/A (F = force, A = cross-sectional area)**

**Strain = e / l (e = extension, l = original length)**

A material subjected to a pair of **opposite forms** might **deform**. A **stress** big enough to **break** the material is called the **breaking stress**. The **maximum stress** the material can withstand is called the **ulitimate tensile stress**. On a graph the **breaking stress (B)** would be the end of the line and the **ultimate tensiles stress (UTS)** would be just before it around where the curve goes slightly down.

**Elastic strain energy** is the **energy stored** in a stretched material. Elastic strain energy is given by the **area under a stress-strain graph**.

You can calculate the **energy stored** in a stretched wire provided it obeys **Hookes law**.

**E = 1/2 Ke2**

## Behaviour of solids

**Brittle**- materials**break suddenly**without plastically deforming. Eg. chocolate bar, ceramics**Ductile**- materials can be**drawn into wires****without losing their strength**. Eg. copper for wires.**Malleable**- materials**change shape**but may**lose their strength**. Eg. Gold, gold rings can be changed shape very easily but a gold bar wouldnt.**Hard**- materials are**very resistant to cutting, indentation and abrasions**. Eg. cutting tool like a chisel, diamond.**Stiff**- materials have a high**resistance to bending and stretching**.**Stiffness is measured by the Young Modulus - the higher the value, the stiffer the material**. Eg. Helmets.**Tough**- materials are really**difficult to break**.**Really tough materials can absorb a lot of energy so are very difficult to break**. Eg. Polymers.

**Stress-strain graphs** for **ductile** materials **curve**. A straight line shows it obeys **Hookes law**, the **limit of proportionality (P)** is the point where the graph starts to curve, the **elastic limit (E)** is where the material wouldnt return to its original length and the **yield point (Y)** is where the material starts to stretch without any extra load.

## Velocity - Time Graphs

The **gradient** of a **Velocity-Time graph** gives you the **acceleration**. The **distance travelled = area under the graph**. Non uniform acceleration (not constant, changing) is a curve on a Velocity-Time graph.

## Displacement - Time Graphs

**Acceleration** means a **curved Displacement-Time Graph**. Different acceleration have different gradients, **bigger** accelerations have **steeper** gradients. **Decreasing** acceleration has the curve going the other way. The **gradient** of a Displacement-Time graph gives you the **velocity** and its the same with **curved lines**, you just have to draw a **tangent**.

**velocity = change in displacement / time taken**

## Streamlines and Flow

**Streamlines** are **stable** flowlines. A flowline is the **path** that a particular **fluid** element takes.

**Streamlines** are **parallel** in **laminar flow**, this usually occurs when a fluid is flowing **slowly**.

Flowlines are **unstable** in **turbulent flow**, this usually occurs when a fluid is flowing **quickly**. In turbulent flow, the fluid often moves around in **miniature whirlpools** - called **eddy currents**.

**Both** types of flow are used in **manufacturing**. Laminar flow, smooth flow is used in **pipes**. Turbulent flow, mixed flow is used in **mixing chemicals**.

**Viscous drag** is the **force of friction** produced by a flowing fluid. Friction **opposes motion**, so the force acts to **slow the flow**. The size of the force depends on the **viscosity** of the fluid - the higher the viscosity, the larger the force. **Viscous drag** is much larger when the flow is **turbulent**.

## Viscosity

**Rate of flow** depends on **viscosity**. The **higher the viscosity** of a fluid, the **slower its rate** of flow. **Viscosity** depends on **temperature**. The viscosity of most fluids decreasess as the temperature increases, fluids generally **flow faster** it they're **hotter**.

**Rate of flow = Volume moved / time taken**

**Viscous drag** acts on objects **moving through fluids**. You can calculate the force due to viscous drag on a sperical object moving through a fluid using **stokes law** -

**F = 6 (pi) n r v**

**(n = viscosity (Nsm-2), r = radius (m), v = velocity (ms-1)**

**(pi) is the mathematical symbol and is equal to 3.14159.**

Fluids exert **upthrust** on **immersed objects**.

**Upthrust = weight of fluid displaced.**

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