An Introduction to Forces: Student Learning Goal The student will analyse, in quantitative terms, the forces acting on an object, and use free-body diagrams to determine net force on the object in one dimension. (B2.9) The student will analyse, in quantitative terms, the forces acting on an object, and use free-body diagrams to determine net force on the object in one dimension. (B2.9)

An Introduction to Forces SPH4C

A Definition A force is a push or a pull.

A Definition A force is a push or a pull. It is a vector quantity and is symbolized by:

A Definition A force is a push or a pull. It is a vector quantity and is symbolized by:

A Definition A force is a push or a pull. It is a vector quantity and is symbolized by: In the SI system, force is measured in Newtons (N). 1 N = 1 kg m/s 2

Applied Force Applied Force is a general term for any contact force, e.g.

Applied Force Applied Force is a general term for any contact force, e.g. Tension Tension

Applied Force Applied Force is a general term for any contact force, e.g. Tension Tension Friction Friction

Applied Force Applied Force is a general term for any contact force, e.g. Tension Tension Friction Friction Normal Force Normal Force

Tension Tension is the force exerted by strings, ropes, cables, etc. attached to an object.

Tension The tension along the string is constant.

Friction Friction acts to oppose any (attempted) motion.

Friction Static friction: the force that prevents a stationary object from starting to move Static friction: the force that prevents a stationary object from starting to move

Friction Friction acts to oppose any (attempted) motion. Static friction: the force that prevents a stationary object from starting to move Static friction: the force that prevents a stationary object from starting to move Kinetic friction: the force that acts against an object’s motion Kinetic friction: the force that acts against an object’s motion

Friction Friction acts to oppose any (attempted) motion. Static friction: the force that prevents a stationary object from starting to move Static friction: the force that prevents a stationary object from starting to move Kinetic friction: the force that acts against an object’s motion Kinetic friction: the force that acts against an object’s motion Air resistance (drag): friction on an object moving through air Air resistance (drag): friction on an object moving through air

Friction Friction acts to oppose any (attempted) motion. Static friction: the force that prevents a stationary object from starting to move Static friction: the force that prevents a stationary object from starting to move Kinetic friction: the force that acts against an object’s motion Kinetic friction: the force that acts against an object’s motion Air resistance (drag): friction on an object moving through air (many physics problems will neglect this) Air resistance (drag): friction on an object moving through air (many physics problems will neglect this)

Normal Force The normal force acts to keep objects apart.

Normal Force The normal force is a force exerted by a surface (or another object) on any other object at 90° (perpendicular to the surface) e.g. if you push on a wall, the wall will exert a normal force on your hand e.g. a table exerts a normal force on a textbook

Action-at-a-Distance Forces There exist forces for which contact between objects is not necessary. These forces are called action-at-a- distance forces.

Action-at-a-Distance Forces There exist forces for which contact between objects is not necessary. These forces are called action-at-a- distance forces.

Action-at-a-Distance Forces There exist forces for which contact between objects is not necessary. These forces are called action-at-a- distance forces. One example is gravitational force, the force of attraction between all objects with mass.

Action-at-a-Distance Forces There exist forces for which contact between objects is not necessary. These forces are called action-at-a- distance forces. Example 1: Gravitational force - the force of attraction between all objects with mass. (The gravitational force the Earth exerts on an object is called its weight.)

Action-at-a-Distance Forces Example 2: Example 2: Electrostatic force – the attractive or repulsive force between charged objects (+ vs. +; + vs. -)

Action-at-a-Distance Forces Example 3: Example 3: Magnetic forces – the force between objects with magnetic poles (i.e. two magnets repel with N-poles facing each other; attract when N-pole facing the S- pole)

Free-Body Diagrams Usually an object will have more than one force acting upon it.

Free-Body Diagrams Usually an object will have more than one force acting upon it. A free-body diagram (FBD) shows all the forces acting on an object

Free-Body Diagrams Usually an object will have more than one force acting upon it. A free-body diagram (FBD) shows all the forces acting on an object – and only the forces acting on the object.

Free-Body Diagrams Usually an object will have more than one force acting upon it. A free-body diagram (FBD) shows all the forces acting on an object – and only the forces acting on the object. A representation of the object is drawn in the centre of the diagram

Free-Body Diagrams Usually an object will have more than one force acting upon it. A free-body diagram (FBD) shows all the forces acting on an object – and only the forces acting on the object. A representation of the object is drawn in the centre of the diagram and the forces acting on it are drawn as arrows pointing outwards.

Free-Body Diagrams Usually an object will have more than one force acting upon it. A free-body diagram (FBD) shows all the forces acting on an object – and only the forces acting on the object. A representation of the object is drawn in the centre of the diagram and the forces acting on it are drawn as arrows pointing outwards. The arrows must be labelled!

FBD: Example 1 A ball is falling downward through the air. Draw a FBD for the ball.

FBD: Example 1 A ball is falling downward through the air. Draw a FBD for the ball.

FBD: Example 1 A ball is falling downward through the air. Draw a FBD for the ball. FgFg

FBD: Example 1 A ball is falling downward through the air. Draw a FBD for the ball. FgFg F air

FBD: Example 2 A book is being pushed rightward across a table. Draw a FBD for the book.

FBD: Example 2 A book is being pushed rightward across a table. Draw a FBD for the book.

FBD: Example 2 A book is being pushed rightward across a table. Draw a FBD for the book. FAFA

FBD: Example 2 A book is being pushed rightward across a table. Draw a FBD for the book. FAFA FfFf

FBD: Example 2 A book is being pushed rightward across a table. Draw a FBD for the book. FgFg FAFA FfFf

FBD: Example 2 A book is being pushed rightward across a table. Draw a FBD for the book. FgFg FNFN FAFA FfFf

An Introduction to Forces: More Practice Draw a free-body diagram for each of the following objects: (a) A car engine being lifted from a car by a rope attached to a pulley

An Introduction to Forces: More Practice Draw a free-body diagram for each of the following objects: (b) an car moving with constant velocity on a level road

An Introduction to Forces: More Practice Draw a free-body diagram for each of the following objects: (c) an apple hanging from a tree branch

An Introduction to Forces: More Practice Draw a free-body diagram for each of the following objects: (d) a skydiver being slowed by a parachute

An Introduction to Forces: More Practice Mr. Wong is pulling across level snow a sled on which is sitting his daughter. Tied to the back of his daughter’s sled is another tiny sled on which his daughter’s baby doll is sitting. Draw the free-body diagrams for (a) Mr. Wong

An Introduction to Forces: More Practice Draw the free-body diagrams for (b) his daughter

An Introduction to Forces: More Practice Draw the free-body diagrams for (d) his daughter’s sled

An Introduction to Forces: Answers to More Practice Draw the free-body diagrams for (d) the doll’s sled

Net Force FBDs are drawn to help determine the net force (the sum of all forces) acting on an object. Resolve all vertical and horizontal vectors and determine the resultant.

FBD: Example 2 with Numbers A book is being pushed across a table with a force of 5 N [right]. The force of friction is 2 N [left], the gravitational force is 10 N [down], and the normal force is 10 N [up]. Find the net force on the book.

FBD: Example 2 with Numbers A book is being pushed across a table with a force of 5 N [right]. The force of friction is 2 N [left], the gravitational force is 10 N [down], and the normal force is 10 N [up]. Find the net force on the book. F g = 10 N F A = 5 NF f = 2 N F N = 10 N

FBD: Example 2 with Numbers A book is being pushed across a table with a force of 5 N [right]. The force of friction is 2 N [left], the gravitational force is 10 N [down], and the normal force is 10 N [up]. Find the net force on the book. Horizontal forces: F A + F f = 5 N + (- 2 N) = 3 N Vertical forces: F g + F N = (- 10 N) + (10 N) = 0 The net force F net = 3 N [right]

I NERTIA AND N EWTON ’ S F IRST L AW OF M OTION

Q UESTION : When you are standing on the train and it suddenly starts to move, what happens? You fall backwards. What happens if you are standing on the train as it is moving and it starts to slow down? You fall forwards. What causes this movement?

I NERTIA A property of matter that causes an object to resist changes in its state of motion; it is directly proportional to the mass of the object. The greater the mass, the greater the inertia an object possesses.

In physics we pretend that there is no friction for some of our problems. If the carpet of the train did not have any friction and there was no air resistance, when the train starts, you would stay in the same spot as the train moves forward until the back wall hits you. When the train slows down, you would continue to move forward until you hit a wall.

N ET F ORCES As we have already learned, several forces can act on one object at the same time. The vector sum of all the forces acting on the object is known as the net force. The net force is not an actual force or a separate force of nature; it is the sum of actual forces.

E XAMPLE : A weight lifter holds a weight above the head by exerting a force of 1.6 kN [up]. The force of the gravity acting on the weight is 1.6 kN [down]. 1. Draw a Free body diagram of the system. 2. Find the net force.

Find the net force. = 1.6 kN [up] kN [down] = 0

N EWTON ’ S F IRST L AW OF M OTION (L AW OF I NERTIA ) If the Net force acting on an object is zero, the object will maintain its state of rest or constant velocity.

T HIS CAN BE STATED IN LAYMAN ’ S TERMS AS : Objects at rest or moving with a constant velocity maintain their state of rest or constant velocity unless acted upon by a net force. The net force must be external in order to change an objects velocity. Internal forces have no effect on an objects motion.

This law of inertia helps us to understand the principles behind using seatbelts and air bags. Once an object is moving, it tends to keep moving at a constant velocity because of its inertia. Air bags and seatbelts help to slow us down safely.seatbelts

E XAMPLE : A 12 passenger jet aircraft of mass 1.6 x 10 4 kg is travelling at a constant velocity of 850 km/h [E] while maintain a constant altitude. Besides gravity and air resistance, the aircraft also experiences an upward force called “lift” and a forward force of the engines called “thrust.” Draw an FBD of the aircraft, and state the net force acting on the aircraft.

What is the net force?

L AW OF INERTIA S UMMARY 1. Objects at rest remain at rest unless acted upon by a net force. 2. Objects in motion remain in motion unless action upon by a net force. 3. If the velocity of an object is constant (or zero), the net external force acing it must be zero. 4. If the velocity of an object is changing either in magnitude, direction, or both, the change must be caused by a net external force on the object.

A T HOUGHT E XPERIMENT You are on a level ice field without boundary Imagine slapping a hockey puck forward and it travels 50 m. 1) What stops the hockey puck? 2) If you smooth out the ice field, what will happen to the travelling distance of the puck? 3) Repeat the above until (theoretically) friction is totally eliminated, what will happen to the travelling distance of the puck? 4) What does that mean?