All Questions
Area in the Unit Square
Find the area of a region in a unit square.
Jacobian
An introduction to the Jacobian
Length of a Curve
Find the length of a line that approaches a given curve.
Limits
Some short limits questions.
Nested Sine
Sketch the curve of a nested sine function.
Root Mean Squared
Find an expression for the root mean sqaure of a sine wave.
Series
Prove some common series equations.
Acceleration in Polar Coordinates
Investigate the terms of acceleration for a particle in a different coordinate system.
Braking Distance
What is the impact of going a little faster on your braking distance?
Car Driving Up a Hill
Investigate the equation of motion for a car moving up a hill.
Centre of Mass of a Can
When drinking a can of a beverage, when is the centre of mass lowest?
Friction along a Path
Investigate some cases of a particle moving on a rough surface.
Lift
How does an aeroplane generate lift?
Mechanical-Electrical Analogies
Investigate how mechanical and electrical systems can be compared.
Newton's Cradle
Investigate the behaviour of a Newton's Cradle when multiple spheres are released at once.
Packing Efficiency
How densely can we pack circles and spheres?
Power Matching
What load resistance maximises the power across the load?
Resistors and Springs
Why do resistors and springs behave differently in series/parallel?
Ring of Charge
What happens when a particle passes through a ring of change?
Rocket Acceleration
Investigate the speed of a rocket ship over time.
Sugar on Scales
What is the reading on a set of scales while sugar is being poured from a height?
Sketch x/(1+x^2)
Sketch the curve y = x/(1+x^2)
Designing a Windmill
Consider the different factors in designing a windmill.
Rollercoaster Loop
How fast does a rollercoast need to go to make it around a loop?
Infinite Resistors
What is the the effective resistance of an infinite combination of resistors?