Forces:Maintaining Equilibrium

or Changing MotionPSE4U

Mr. MacMillan

Something to Think About

O A gymnast maintains a position on one foot during a balance beam routine. A rock climber clings by her fingertips to the face of a cliff.

O What are the forces that act on each of these athletes?

O How do athletes manipulate these forces in order to maintain balance?

What are Forces?O A force is a push or pullO They are exerted by objects on other

objectsO A force is something that accelerates or

deforms an object.O A force is measured is a Newton

O This is named after Sir Isaac NewtonO 1 N of force is defined as the force

required to accelerate 1 kg mass 1 m/s/sO 1.0 N = (1.0 kg)(1.0 m/s/s)

Classifying ForcesO Internal Forces

O Are forces that act within the object or system whose motion is being investigatedO Internal pulling forces – tensile forcesO Internal pushing forces – compressive

forcesO Examples of internal forces

O Muscles

O External ForcesO Forces that act on an object as a

result of it’s interaction with the environment surrounding it

O Examples of external forcesO The force of gravityO Magnetic forcesO Electrical forces

O WeightO The force of gravity acting on an

objectO W = mass x acceleration due to

gravity = m x g (9.81 m/s/s)

O To estimate the weight of something you multiply its mass by 9.81.

Contact ForcesO Forces that occur between objects in contact

with each otherO Examples: Air resistance, water, reaction forces

O Static FrictionO Dry friction between two surfaces that are not

moving relative to each otherO Also referred to as limiting friction

O Dynamic frictionO Dry friction between two surfaces that are

moving relative to each otherO Also known as sliding friction and kinetic friction

Self-ExperimentO Lets do some experimentation to learn more

about friction. Place a book on a flat horizontal surface such as a desk or tabletop. Now push sideways against the book and feel how much force you can exert before the book begins to move.

O What force resists the force that you exert on the book and prevents the book from sliding?O Static frictionO If the book doesn’t slide then the static friction

force acting on the book is the same size as the force you exerted on the book.

O Now add another book on top of the original and push again.O Can you push with a greater force

before the book begins to move?O Add another book. What happens?

O As you add books to the pile, the magnitude of the force you exert before the books slide becomes bigger and so does the static friction force

O Mathematically we can express static and dynamic friction as:

O Static: Fs = usRO us = coefficient of static friction O R = normal contact force

O Dynamic: Fd = ud RO ud = coefficient of dynamic friction O R = normal contact force

Adding of Forces: Force Composition

O Forces are added using the process of vector addition

O The result of vector addition of two or more forces is called a resultant force

O The vector addition of all the external forces acting on an object is the net force.

O Colinear Forces are forces that have the same line of action.

Sample ProblemO A spotter assists a weightlifter who is

attempting to lift a 1000 N barbell. The spotter exerts an 80 N upward force on the barbell, while the weight lifter exerts a 980 N upward force on the barbell. What is the net force exerted on the barbell?

O Total Force = 80 N + 980 N + (-1000 N) = 60 N

O The net vertical force acting on the barbell is a 60 N force acting upward

Concurrent ForcesO Do not act along the same line, but

they do act through the same pointO i.e. a gymnast on the high bar

Sample ProblemO A gymnast jumps up and grasps the high bar and his

coach stops his swinging by exerting forces on the front and back of the gymnast’s torso. The external forces acting on the gymnast are the force of gravity acting on the mass of the gymnast, a horizontal force of 20 N exerted by the coach pushing on the front of the gymnast, a horizontal force of 30 N exerted by the coach on the back of the gymnast, and an upward vertical reaction force of 550 N exerted by the bar on the gymnast’s hands. The gymnast’s mass is 50 kg.

O What is the net external force acting on the gymnast?

Free-body Diagram

20 N 30 N

W = 500 N

O First, how large is the force of gravity acting on the gymnast?

O W = mgO = (50 kg)(10 m/s/s) = 500 kg m/s/s

= 500 N

Scale DrawingO Using an appropriate scale, draw all forces

550 N500 N

30 N

20 N

Resultant force 51 N

50 NResultant Force 51 N

10 N

Trigonometric Technique

O A2= B2 + C2

O Pythagorean theoremO Sample ProblemO The vertical ground reaction force

(normal contact force) acting under a runners force is 2000 N, while the frictional force is 600 N acting forward. What is the resultant of these two forces?

1. Draw the forces2. Draw the resultant force3. Compute the resultant force

Weekend Assignment1. Research a career in the field of biomechanics2. Give a one paragraph description of the career you

chose3. Find out what qualifications you need for the job and

describe the program(s) you may need to take in college/university and/or special training

4. List 3 schools where you can get these qualifications 5. Find the average salary and, if there is one, a pay

scale for the profession6. What is the job prospects in the future? Are there

any available jobs? Find an advertisement online to support your claims.