Outline

# GeoGebra Apps for A-Level Mechanics including FM

## Table of Contents

### Drawing motion graphs:

- The displacement of a moving particle.
- Drawing a displacement-time graph of a moving particle.
- Negative displacement of a displacement-time graph
- Motion of a ball thrown upwards.
- Velocity-time graphs acceleration and displacement.
- Displacement, velocity, acceleration time graphs
- Displacement vs distance on a velocity-time graph
- Speed from a velocity-time graph

### Motion in a straight line with constant acceleration:

- Motion of a particle in a straight line part b
- Constant versus variable acceleration.
- Kinematics of a particle moving in a straight line with a constant acceleration.
- Kinematics: A drone moving in straight line.
- Finding when one particle overtakes another particle on a straight line
- Finding uniform acceleration and initial velocity using simultaneous equations.
- Finding uniform acceleration and initial velocity using simultaneous equations.
- Finding uniform acceleration and initial velocity of a particle passing posts

### Vertical motion in a straight line under gravity:

### Forces and Newton's laws of motion:

- Forces on a falling ladder from a brick wall.
- The forces on a ball in the air.
- Finding the tension in the couplings of a toy train
- Forces on a man and a lift moving upwards and downwards.
- Forces on a man and lift with reaction graph
- Forces on a man and lift with velocity-time graph
- Connected objects in a pulley system
- A pulley problem with a velocity-time graph
- Resolving a two pulley system.
- A block on a rough table connected to another block by a smooth light pulley
- Connected objects with vertical motion under gravity
- Distance of a block that comes to rest from top of a slope
- A box moving along a horizontal smooth and rough plane
- A box moving along a smooth and rough inclined plane

### Variable acceleration:

- Variable acceleration introduction.
- Motion of a particle in a straight line part b
- Displacement, distance, velocity and acceleration.
- Using differentiation to describe the motion of a particle
- The distance of a particle P from the origin O.
- Determining whether a particle changes direction using velocity
- Kinematics introduction.
- A moving particle on a straight line.
- A moving particle P
- Kinematics variable acceleration with a piecewise function
- Determining the direction of two particles moving along a straight line

### Projectile motion:

- The general equations of a projectile.
- A model for a projectile launched from a building.
- Finding the angle of projection given the range.
- Hitting a boat on water using projectile motion
- The bounding parabola for projectile motion.
- Projecting a particle P on a uniform slope
- Projecting a particle P downwards on a uniform slope.
- Projecting a particle P downwards on a uniform slope.
- Determining whether a projectile hits a wall given u and y_max
- The path of a cricket ball

### Motion in two or three dimensions:

### Force and motion:

- Resolving forces on a block inclined when in equilibrium
- The forces block suspended from P and Q and angle is 90 degrees
- A block suspended by a light string showing components.
- Finding the resultant of a system of forces.
- Resolving forces on a block moving up a slope.
- Particle on a rough slope leading to projectile motion.
- Which way to draw the frictional force for a block to be in equilibrium.

### Work, energy and power:

- Work done against gravity.
- The total work done in moving a block horizontally
- Work done against gravity and friction.
- Finding velocity using the Principle of Conservation of Energy
- Finding height using the Principle of Conservation of Energy.
- The conversation of the energy of a particle moving down a slope
- Conservation of energy for a swing
- Energy gained by a block being winched up a rough slope.
- Finding the power of a car acending a hill with a constant velocity.
- The power needed by a pump raising and ejecting water.

### Moments of forces:

### Impulse and momentum:

### A model for friction:

### Centre of mass 1:

- The centre of gravity of a coordinate system.
- The centre of gravity of a rectangular lamina.
- Finding the centre of mass of a uniform 2D body.
- Finding the centre of mass metal disc with a hole.
- The centre of mass of a uniform triangular lamina.
- Sliding and toppling of a uniformed block
- Sliding and or toppling of a uniform block with dimensions
- Centre of mass: The leaning tower of Lire

### Circular motion:

- Circular motion - angular speed
- The acceleration of a body moving with uniform motion on a circular path.
- A car and police car moving with the same angular speed.
- A model for a conical pendulum
- A car on a circular banked track
- Motion in a vertical circle.
- The reaction force R of a bead threaded on a smooth vertical circular wire.
- The motion of a particle from rest on the top of a smooth sphere.

### Hooke's Law:

- Finding the extension of a particle P using Hooke's law
- Finding the extension of a light elastic spring by a mass on a slope.
- The compression of a spring after a collision.
- Using Hooke's law with more than one elastic string
- Work and energy using Hooke's law for vertical motion
- The mechanics of a catapult using Hooke's law

### Differential equations:

- The limiting value of a differential equation 01.
- The limiting value of a differential equation 02.
- Solving a differential equation for an electrical circuit.
- Second order differential equations damped oscillations
- Non-homogeneous 2nd order differential equations
- Modelling a bungee jump with a 2nd order differential equation.
- The steady state response of a damped second-order system
- Solving a 2nd-order differential equation using Laplace transformations
- The differential equation of a damped system
- Damped vibrations with graphs
- Differential equation solution of a mass being projected upwards
- Solution of a 1st order differential equation with slope field.
- Graphical solution of a 2nd-order differential equation

### Simple harmonic motion:

- Simple harmonic motion introduction.
- Modelling UK tides using simple harmonic motion
- Simple harmonic motion of a mass fixed by two elastic strings
- A suspended vertical spring in simple harmonic motion.
- Simple harmonic motion of a mass on a vertical elastic string fixed to two points
- Simple harmonic motion as a function of time

### Centre of mass 2:

- The centre of gravity of combined hemisphere and cone.
- Volume of revolution introduction.
- Finding the centre of mass for a uniform 3D mass.
- Finding the centre of mass of a solid hemisphere of radius r
- Finding the centre of mass of a solid cone radius r, height h.
- Finding the centre of mass of a hollow bowl.
- Finding the centre of mass of a lamina plane introduction.
- The centre of mass of a lamina bounded by a quadratic, x = a and x = b
- The centre of mass of a lamina between two curves.

### Oblique impacts: