1. Forces and Free-Body Diagrams
Text Reference
Section 2.1

2. FORCE
is an applied push or pull on an object causing acceleration, compression, stretching, twisting, and/or stabilization

3. Force of Gravity (Weight)
is the force of attraction between all objects acting downwards toward the centre of the Earth

4. NORMAL FORCE
is the force the acts perpendicular to the surfaces that are in contact with the object

5. TENSION FORCE
is the force exerted by stretchable materials like ropes, fibers, springs, cables, etc.
is always directed away from the body being pulled and has the same magnitude throughout the length of the material
force increases when the material’s stretch-ability increases

6. FRICTIONAL FORCE
is the force that resists motion between objects in contact
always acts in the opposite direction to the direction of motion of the object
is a function of the nature and weight of the two surfaces in contact (and not on speed or surface area of contact)
there are 3 types

7. STATIC FRICTION
is the force that prevents stationary objects from starting to move
measured in Newton
is the product of the normal force measured in Newton and the static coefficient of friction which has no units
Note that the static coefficient is greater than the kinetic coefficient of friction.

8. KINETIC FRICTION
is the force that resists the motion of moving objects
measured in Newton
is the product of the normal force measured in Newton and the kinetic coefficient of friction which has no units
Note that once the object is moving, kinetic and not static coefficient must be used.

9. AIR RESISTANCE
is the force that resists the motion of flying or falling objects in the air
measured in Newton
is noticeable at high speeds
is opposite to the direction of motion
is a function of the object’s velocity squared

10. Free Fall and Terminal Velocity
Accelerating – speeding up when parachute is closed (force of gravity is greater than force of air resistance).
Terminal Velocity occurs when object falls at a constant speed when both forces are in balance. Note that every object has a different terminal velocity.
Decelerating – slowing down when parachute is opened (force of gravity is less than force of air resistance).

11. Diagrams: SYSTEM DIAGRAM:
A sketch that includes all items and objects in the scenario.
FREE-BODY DIAGRAM:
A picture comprised of a circle or square with a dot in the centre to represent ONE of the objects in the system.
All forces acting on that particular object are drawn outward from the dot.

12. Example of a FBD:
OBJECT on a FLAT SURFACE:
OBJECT on a RAMP:

13. Find the resultant force for an object with the following forces acting on it: 197 N [up], 198 N [down], 25 N [right] and 24 N [left].
Two students are trying to pull a 20 kg toboggan out of a deep snow drift that provides an opposing force of 8.0 N. They are using ropes attached to the toboggan that are parallel to the ground. The forces exerted by the students and the directions in which they pull on the ropes are 20 N at 30° and 15 N at 20° from the forward horizontal direction. What is the acceleration of the toboggan?
The driver of a 2000 kg car applies the brakes on a dry concrete roadway. Calculate the force of friction between the tires and the road surface.
A 20 kg box is dragged across a level floor with a force of 100 N. The force is applied at an angle of 40° above the horizontal. If the coefficient of kinetic friction is 0.32, then what is the acceleration of the box?
A student on a toboggan is sliding down a snow-covered hillside. The student and toboggan together have a mass of 50 kg and the slope is at an angle of 30° to the horizontal. Find the student’s acceleration:
Assuming that there is no friction.
Assuming that the coefficient of kinetic friction is 0.15.

14. Newton’s First Law of Motion: The Law of Inertia
INERTIA is the ability of an object to resist changes to its motion. The greater the mass, the greater the inertia of an object.
If the net force acting on an object is zero, then that object maintains its state of rest (static equilibrium) or motion at constant velocity (dynamic equilibrium).
There is NO acceleration because the forces are in BALANCE.

15. Newton’s Second Law of Motion: FNET=ma
If the external net force acting on an object is NOT zero, then the object accelerates in the direction of the net force.
The acceleration is directly proportional to the net force and inversely proportional to the object’s mass.
The system has an ACCELERATION because the forces are UNBALANCED.

16. Example #1: Static Equilibrium
A clothes-line is attached to high poles 10.0 m apart. A pulley allowed to roll freely on the line has a 30 kg mass hanging from it. Find the tension in each half of the clothes-line if the sag at the centre is 0.40 m.

17. Example #2: Dynamic Equilibrium and Acceleration of the System
A baby carriage with a mass of 50 kg is pushed along a rough sidewalk with an applied horizontal force of 200 N and is moving at a constant velocity of 3.0 m/s.
What is the force of friction?
What is the applied horizontal force required to accelerate it from rest to 7.0 m/s in 2.0 s?
What is the applied force required to accelerate it from rest to 7.0 m/s in 2.0 s if the force was applied at an angle of 30° from the horizontal?

18. Newton’s Third Law of Motion: The Law of Action-Reaction
For every action force, there is a simultaneous reaction force that is equal in magnitude, but opposite in direction.
Sometimes this force may be fictitious, for example, centripetal force and centrifugal force.
These law deals with solving tension problems!!!

19. Example #3: Pulley Systems
A toy train consists of 3 carts joined together by 2 short strings and with a longer string for pulling which is attached to cart 1. If a child pulls the toy with a horizontal force of 6.0 N, then what force must each of the short strings be able to withstand? The total mass is 3.0 kg where cart 3 is 1.0 kg, cart 2 is 1.5 kg, and cart 1 is 0.5 kg.
A pulley has a mass of 6.0 kg on one end and a mass of 8.0 kg on the other end. What is the acceleration of the 6.0 kg mass? What is the tension in the string?
A mass of 6.0 kg is on a table and is pulled by 8.0 kg mass hanging at the end of the table on a pulley. What is the acceleration of the 6.0 kg mass? What is the tension in the string?

20. Examples continued: Pulley and Ramps with Friction
A mass of 5.0 kg is on a table and is pulled by 2.0 kg mass hanging at the end of the table on a pulley.
What is the static coefficient of friction such that the system is just about to move?
What is the acceleration of the system if the coefficient of kinetic friction is 0.20? What is the tension in the rope?
A mass of 5.0 kg is on a ramp and is pulled by 4.0 kg mass hanging at the end of the ramp on a pulley. The ramp has an incline of 25°.
What is the acceleration of the system if the coefficient of kinetic friction is 0.2?
What is the coefficient of static friction that will just prevent the block from sliding up?