Unit Two: Dynamics

Section 1: Forces

Look in glossary of book … What is the difference between dynamics and

kinematics? What is a force? What can a force do? What

causes a force?

Key Terms: Dynamics Kinematics Force Gravitational Force Strong Nuclear Force Inertia Net Force Normal Force Weight Mass

What is dynamics???

Kinematics: The study of how objects move (velocity, acceleration) Galileo performed experiments that allowed him

to describe motion but not explain motion. Dynamics: The study of why objects

move. The connection between acceleration and its

cause can be summarized by Newton’s 3 Laws of Motion (published in 1687)

The cause of acceleration is FORCE.

Forces

What is a force? A push or a pull

Some forces cause acceleration Example: gravity

Some forces cause stretching, bending, squeezing Example: spring force

The 2 Main Types of Forces Contact Forces: are forces that result whentwo objects are physically in contact with one another

Example: push/pull, normal force, friction, spring force, tension, air resistance

Non-contact Forces: forces that result when two objects are not in physical contact

Example: gravitational force, nuclear force, magnetic force, electrostatic force (electric charge)

Newton’s First Law of Motion- Newton’s Law of Inertia

An object at rest or in uniform motion (ie, constant velocity) will remain at rest or in uniform motion unless acted on by an external force.

Section 5.1 in text (pages 154 to 159) Reworded: An object at rest will remain at rest until

a force is applied. An object moving at a constant velocity will continue to move at a constant velocity if no force is applied (ie, no acceleration).

Inertia

the natural tendency of an object to remain in its current state of motion (either moving or at rest)

Where did this come from?

Galileo performed many experiments and speculated that if a perfectly smooth object were on a perfectly smooth horizontal surface it would travel forever in a straight line.

Newton developed this idea.

Newton’s First Law Example

If an apple is sitting on Mrs. Evans’ desk, it will remain there until the desk is removed (so gravity acts on it) or someone lifts it up (applied force).

If a car is driving along a straight road at 100km/h, it will continue to do so (given the car still has gas!) until the brakes are applied (applied force), there is a turn or the road surface changes (more or less friction).

Net Force

The sum of all vector forces acting on an object.

Example: What are the forces acting on a stopped car? Draw a labeled diagram.

Example: What are the forces acting on a car moving at 100km/h [N]?

Normal Force

A force that acts in a direction perpendicular to the common contact surface between two objects

Example Diagram:

Quick Experiment

Materials – cup, card, penny or coin

What to do:

Set up the card on top of the cup and the penny on the card in the middle.

Flick the card. What happens to the card? The penny? Why?

Questions

1. To which object was a force applied by the flick and which object was not acted upon by the flick?

2. Why did the penny fall into the cup and not fly off with the card?

3. What force held the penny in place while the card was flicked out? What force brought the penny down into the cup?

4. Would the penny move in the same way if sandpaper was used instead of the card?

Summary

The inertia of every object resists the change in motion. In this case, the inertia of the penny held it in place while the card was flicked out from under it. The force acting on the card was not applied to the penny. After the card was moved from under the coin, gravity supplied the force to bring the penny down into the cup. If a force had been applied to both the card and the penny, then both would have moved and the penny would not have fallen into the cup.

Check Your Learning

1. Why does a package on the seat of a bus slide backward when the bus accelerates quickly from rest? Why does it slide forward when the driver applies the brakes?

Use as many physics terms as possible and describe in detail.

The bus is initially at rest, as is the package. In the absence of any force, the natural state of the package is to remain at rest. When the bus pulls forward, the package remains at rest because of its inertia (until the back of the seat applies a forward force to make it move with the bus).

From the point of view of someone on the bus, it appears that the package is moving backward; however, someone watching from outside the bus would see the bus move forward and the package trying to stay in its original position.

Once the package is moving with the bus, its inertia has now changed. It now has a natural tendency to be moving forward with a constant speed. When the bus slows down, the package continues to move forward with the same constant speed that it had until some force stops it.

Force

Symbol: F

Formula: F=ma

Force = mass x acceleration

Units: kg x m/s2 = Newtons (N)

Gravitational Forces

Example: Consider the following information and then compare the gravitational force on the SAME OBJECT in each case. A man standing near the equator (distance from

Earth’s centre = 6378 km) A man standing near the North pole (distance

from Earth’s centre = 6357 km) A man standing in the International Space Station

(distance = 6628 km) A man in a space ship past Pluto

Gravitational Forces

Gravitational force decreases as we increase how far we are from the centre of the Earth

It is a non-contact force

Weight Vs. Mass

Weight and mass are NOT THE SAME.

Weight = the force of gravity acting on a mass. Weight can change. It is measured in Newtons (force). Weight = mass x gravitational force Fg = mg

Mass = the quantity of matter an object contains. Mass for the same object is constant. It is measured in kg.

Weight Can Change…

Examples of Weight Problems

Mrs. Evans’ dog Pi has a mass of 17kg. What would Pi’s weight be:

A) On Earth? B) On Jupiter (where g = 25.9 m/s2) C) On the Moon (where g = 1.64 m/s2)

Examples of Weight Problems

A student standing on a scientific spring scale on Earth finds that he weighs 825N. Find his mass.

Practice

Page 137, #1, 2, 3, 4

Friction

A contact force

Electromagnetic Force (between surface atoms of objects touching)

Friction

There are 2 types of friction: Static Frictional Force

When you start to move an object from rest Larger than Kinetic Frictional Force due to Inertia ųs

Kinetic Frictional Force Exists when the object is moving ųK

Friction

The strength of friction depends on… Surface materials Magnitude of forces pressing surfaces together

The strength of friction DOES NOT depend on… Surface area Velocity of object moving

See page 140, table 4.5 for a list!

Coefficient of Friction

“Stickiness value” ų (symbol mu) ų has no units

Page 140, table 4.5

Formula: Ff = ųFN

Remember: FN = - Fg

Friction Example

During the winter, owners of pickup trucks often place sandbags in the rear of their vehicles. Calculate the increased static force of friction between the rubber tires and wet concrete resulting from the addition of 200. kg of sandbags in the back of the truck.

Use the table of coefficients of friction on page 140.

Friction Example 2

A horizontal force of 85N is required to pull a child in a sled at constant speed over dry snow to overcome the force of friction. The child and sled have a combined mass of 52 kg. Calculate the coefficient of kinetic friction between the sled and the snow.

Practice Friction Problems

Page 144 Questions 5, 6, 7, 8

Weight Problems

Page 137, #1, 2, 3, 4

Tug of War

Sometimes we have more than 1 force acting on an object (like in a tug of war).

What are the forces at work in a tug of war? What direction are the forces? If your team wins, what does that mean about

the forces? If your team loses, what does that mean

about the forces? What other forces are there on the players?

Free Body Diagrams

We usually use a box or small circle to represent the object.

The size of the arrow is reflective of the magnitude (SIZE) of the force.

The direction of the arrow reveals the direction in which the force acts.

Each force arrow in the diagram is labelled to indicate the type of force.

Use math symbols to show equality if needed.

What can you tell about these forces??? What else could we add?

Free Body Diagrams

A free body diagram will be used in most dynamics problems in order to simplify the situation

In a FBD, the object is reduced to a point and forces are drawn starting from the point

Fg

FN

Fa

Ff

Free Body Diagram Examples

1. A book is at rest on a table top. Diagram the forces acting on the book.

Refer to sheet in class with 10 examples!

The Net Force

The net force is a vector sum which means that both the magnitude and direction of the forces must be considered

In most situations we consider in Physics 11, the forces will be parallel (ie, up and down, etc) and perpendicular

The Net Force In most situations, there is more than one

force acting on an object at any given time When we draw the FBD we should label all

forces that are acting on an object and also determine which would cancel each other out

Ones that do not completely cancel out will be used to determine the net force

Find the net force on each FBD

Find the net force on the FBD

FBD and Net Force Mini Worksheet

Newton’s Second Law Newton’s first law states that an object does not

accelerate unless a net force is applied to the object.

But how much will an object accelerate when there is a net force? The larger the force the larger the acceleration. Therefore acceleration is directly proportional to mass.

Acceleration also depends on mass. The larger the mass, the smaller the acceleration. Therefore acceleration is inversely proportional to mass. We say that a massive body has more INERTIA than a less

massive body.

Newton’s Second Law- Newton’s Law of Motion

Force = mass x acceleration

Fnet = ma

The acceleration is in the same direction as the force.

Newton’s Second Law Examples

Ex. 1: What net force is required to accelerate a 1500. kg race car at +3.00m/s2?

Draw a FBD to show the net force.

Practice Problems

Page 163, Questions 1, 2, 3

Putting it All Together

Now that we have considered Newton’s Second Law, you can use that to analyze kinematics problems with less information than we have used previously

We can either use dynamics information to then apply to a kinematic situation or vice versa

Newton’s Second Law Examples

Ex. 2: An artillery shell has a mass of 55 kg. The shell is fired from a gun leaving the barrel with a velocity of +770 m/s. The gun barrel is 1.5m long. Assume that the force, and the acceleration, of the shell is constant while the shell is in the gun barrel. What is the force on the shell while it is in the gun barrel?

Practice Problems

Page 168, questions 4 to 8

An Example

A 25kg crate is slid from rest across a floor with an applied force 72N applied force. If the coefficient of static friction is 0.27, determine: The free body diagram. Include as many of the

forces (including numbers) as possible. The acceleration of the crate. The time it would take to slide the crate 5.0m

across the floor.

FBD

Fg=-250N

FN=250N

Fa=72NFf=?

Use the frictional force equation to determine the magnitude of the frictional force

NF

NF

NF

FF

f

f

f

Nf

66

66

)250)(27(.

The net force is the sum of the forces (acting parallel or anti-parallel)

NF

NNF

FFF

FF

net

net

afnet

inet

8.5

7266

Use Newton’s Second Law to solve for the acceleration

2/23.0

)25(8.5

sma

akgN

amFnet

Use kinematics to solve for the time taken to cross the floor

stsm

mt

tsmm

dtvta

td

6.6/23.0

)0.5(2

2

/23.00.5

2)(

2

22

00

2

Example 3

A baby carriage with a mass of 50. kg is being pushed along a rough sidewalk with an applied horizontal force of 200. N and it has a constant velocity of 3.0 m/s.

A) What other horizontal force is acting on the carriage and what is the magnitude and direction of that force?

B) What value of applied horizontal force would be required to accelerate the carriage from rest to 7.0 m/s in 2.0 s?

Example 3

A) Force of friction must be equal in magnitude (so 200.N) in the opposite direction to the force applied (of the baby carriage moving forward).

B) First find a using a = (vf – vi)/t = 2.0m/s2

Now find Fnet = ma = 50x2 = 100N Now use Fnet = Fapp – Ff Fapp = 300N = 3.0 x 102 N

Example 4

A horizontal force of 50. N is required to pull an 8.0 kg block of aluminum at a uniform velocity across a horizontal wooden desk. What is the coefficient of kinetic friction?

Example 4

You know that Force of friction is equal and opposite to Force applied. Therefore, Ff = 50.N.

You know that Force of friction = coefficient of friction x normal force.

Normal Force = - Force of gravity = -mg Fn = 78.48N Sub in and rearrange to find that coefficient =

0.64 (no units)

Example 5

A 75 kg man stands in an elevator. Draw a free body diagram and determine what the force the elevator exerts on him will be when

A) the elevator is at rest B) the elevator is moving upward with a uniform

acceleration of 2.0 m/s2 C) the elevator is moving downward with a uniform

velocity of 2.0 m/s D) the elevator is moving downward with a uniform

acceleration of 2.0 m/s2

Example 5

A) Fnet = 0N, Fapp = 0N B) Fnet = 150N [up] C) Fnet = 0N D) Fnet = 150N [down]

Practice Problems

Page 170 9, 10 and 13

System of Masses When two or more masses are attached by a string

or rope and hang over a pulley system, there is a system of masses.

Some assumptions that must be made: - Strings only exert pulling forces. - The tension in the string is the same throughout its

length. - A frictionless pulley changes the direction of a

string without diminishing its tension. - Strings do not stretch. - The strings’ mass is negligible.

Tension

Tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object.

It is measured in Newtons It is measured parallel to the string on which

it applies

Example 1

A 2.0 kg mass, placed on a smooth, level table is attached by a light string passing over a frictionless pulley to a 5.0 kg mass hanging freely over the edge of a table.

A) Draw a free body diagram of the masses B) Calculate the tension in the string C) Calculate the acceleration of the 2.0 kg

mass

Answer

Answer continued

The masses move together – so the accelerations are the same!

The forces are slightly different. How?

Ask yourself how the system will move: First, we know that mass m is falling and

dragging mass M off the table. The force of kinetic friction opposes the motion of mass M. However, we know that friction is negligible here because it is a smooth surface!

We also know, since both masses are connected by a nonstretching rope, that the two masses must have the same speed and the same acceleration.

Example 2

Two spheres of masses 1.5 kg and 3.0 kg are tied together by a light string looped over a frictionless pulley. They are allowed to hang freely. What will be the acceleration of each mass?

http://schools.hwdsb.on.ca/highland/files/2011/01/System-of-Connected-Masses.pdf\

Systems of Masses Worksheet

Newton’s Third Law

When one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude but opposite in direction.

These forces are called action-reaction forces. Ex: If you push against a wall, you don’t go through

it as the wall “pushes back”.

Only the forces on an object determine its acceleration.

Newton’s Third Law

• With equal and opposite forces, how does anything ever move?

Example: Picking up a ball:

Ball exerts an equal force on your hand, but this is not on the ball and does not appear in the free body diagram

Example

Suppose you are floating around in space (many km from any planet so that you feel no gravity) outside of your spaceship. You get frustrated and decide to kick your spaceship. Does your foot hurt?

Solution

Yes, your foot will hurt. Even though there is no gravity, Newton’s Third law still applies. If you kick the spaceship, it applies an equal and opposite force on your foot.

Newton’s Third Law Worksheet

Inertial Frame of Reference

A frame of reference that is at rest or moving at a constant velocity.

Example: You moving in a car on cruise control.

Example: You sitting at your desk. Newton’s Laws of Motion are valid here!

Non-inertial Frame of Reference

An accelerating frame of reference Example: When you suddenly stop in a car. Example: When you are speeding up and

passing a car.

Newton’s Laws of Motion do not apply!

Read pages…

Frames of Reference

Imagine you are driving in a car. Does it feel like you have moved?

If you are watching from the road, how does your frame of reference change?

What type of frame of reference???

You are standing in an elevator waiting for it to go up 10 flights.

You are standing in an elevator that is just starting to move.

You are standing in an elevator going down at a constant speed.

There are two kinds of mass.

1. Inertial mass: the ratio of the net force exerted on the object and its acceleration.

2. Gravitational mass: the comparison of gravitational forces of two masses (one with a known mass, the other with an unknown mass)