MECHANICS 1 & 2 October 2015 Why 1 & 2? Keeps in line with existing University scheme of 11 lectures.

Overview 10 lectures involving – Key points – Practice questions – Simple experiments Notes are on Learnzone Maps closely onto the textbook, units 9 – 12, 26 and 28.

Overview of Mechanics – ten lectures in IFP Physics Semester 1 Unit refers to the textbook. We follow this quite closely. Exam questions may come from here!

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Forces What can forces do? Push, Pull or twist an object Contact and non-contact forces: – E.g. Direct touch OR magnetic forces At this level we mainly talk about idealised, uncompressible objects For these idealised objects a net force will change the object’s motion

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Representing Force Vectors Can be drawn as an arrow- length = magnitude, Direction also shown. We often want to combine vectors to find the resultant (net) vector.

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Vectors and Scalars SCALARS Have a magnitude only Examples: – Temperature – Energy – Distance – Speed – time VECTORS Have a magnitude and a direction. How to specify direction? NSEW, bearing, up/down… Examples – Velocity, – Force, – Acceleration – Displacement

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Combining vectors graphically 1. Head-to-tail (Polygon method)

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Combining vectors graphically Parallelogram method A common mistake

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque FORCE SUBTRACTION Just flip one of the vectors around and then add them up. A – B = A + (-B)

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Practice (Breithaupt p 116 Q9.1 a)

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Resolving a vector Just as we can combine any two vectors into one, we can also split any vector into two components at 90⁰ to each other. Very useful! E.g. for projectile motion

Techniques Scale Drawing Trigonometry Pythagoras θ A 1. Components A x A y 2. A in terms of A x and A y 3. Θ in terms of A x and A y

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Combining several vectors If you have several vectors, – Resolve them all into x and y components – Add up all the x components then all the y components

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Trying this out – Practice - 9.1b. – Worked example 9.1

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Equilibrium A body is in equilibrium if all the forces acting on it sum to zero. Graphically, all the force vectors would form a closed polygon.

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Turning forces

What’s wrong with this picture? What features can we identify?

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Simple experiments… What’s the relationship for… 2 Equal masses 2 unequal masses More than 2 masses

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Lead to idea of moments A moment is the turning effect of a force. The moment of the force is the force * distance. but note… It is the perpendicular (shortest) distance. Full definition… “ the moment of a force about any point is the force x the perpendicular distance from the line of action of the force to the point.”

In pictures

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque And the principle of moments For a body in equilibrium, Sum of clockwise moments = sum of anticlockwise moments. This works about any point But it is usually best to choose the pivot or another obvious point like a support

Practice questions Start by drawing a neat scale diagram

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Examples – look at in your own time Worked Example 9.2 Questions 9.2, no 1 and 2.

It’s the perpendicular distance that is measured moment

Last bit! Defining a couple So the moment of the couple is F * d/2 + F * d/2 (both act to produce an anticlockwise moment) So moment = Fd wheel.

Objectives Define vectors and scalars Combine and resolve vector and scalar quantities Define equilibrium of a body Apply the principle of moments to solve problems Key Words Force, Vector, Resolve, combine, equilibrium, moment, couple, torque Want a high grade? Work through Breithaupt pp before the next lesson