Motion & Force: Dynamics

Physics 11

Galileo’s Inertia Galileo attempted

to explain inertia based upon rolling a ball down a ramp

Predict what would happen in each of the following situations:

Forces and Motion

Predicting the motion of an object is known as kinematics and as we have seen in the previous section, result in the equations of motion

Now, we will begin to consider the forces that act on an object to

describe the why of motion; this is known as dynamics

Inertial Mass

Inertia is often understood as the resistance of an object to a change in its motion

Inertial mass is used to describe this property of an object

Another type of mass, gravitational mass, describes the attraction between massive objects

Fundamental Forces

There are four forces that result in the behaviours we observe in the Universe: Gravitation Electromagnetic Strong Nuclear Weak Nuclear

Gravitation All massive objects attract other

massive objects This means that the Earth exerts a

force on you (toward the centre of the Earth) but at the same time, you exert an equal and opposite force on the Earth

Because the mass of the Earth is significantly larger than your mass, your acceleration toward the Earth is much greater than the Earth’s acceleration toward you

Weight vs. Mass Although mass and weight are used

interchangeably in common vernacular, from the standpoint of scientific language, this is not correct

Mass is the measure of the amount of matter in an object and does not change; it is measured using a balance

Weight is the measure of the gravitational attraction between objects and can change; it is measured using a spring scale

Weight vs. Mass

Although they are different, weight and mass are related using the following equation:

gmFg

Newton’s 1st & 2nd Laws of Motion

Physics 11

Newton’s Laws

There are three laws that Newton used in Principia in order to explain motion

What are the three laws?

Newton’s Laws of Motion

1. An object at rest or in uniform motion will remain rest or in uniform motion unless acted on by an external force.

2. Acceleration is directly proportional to the force applied to an object and inversely proportional to its mass.

3. For every action, there is an equal and opposite reaction.

Newton’s Laws of Motion

1. An object at rest or in uniform motion will remain rest or in uniform motion unless acted on by an external force.

2. Acceleration is directly proportional to the force applied to an object and inversely proportional to its mass.

3. For every action, there is an equal and opposite reaction.

Inertial and Non-Inertial Frames of Reference

An inertial frame of reference is one in which Newton’s Laws are valid

An inertial frame is either at rest or in uniform motion but they are no accelerating

A non-inertial frame of reference is one in which Newton’s Laws are not valid

Accelerating frames of reference are always non-inertial

Newton’s Second Law

Acceleration is directly proportional to the force applied to an object and inversely proportional to its mass.

amF

Friction

Physics 11

Friction

Friction is a contact force and occurs when one object moves or is attempted to be moved across another

Based upon physical properties, it is possible to determine the maximum amount of frictional force that can be present but friction only acts to oppose motion

Static vs. Kinetic

Static frictional forces exist when there is no motion

Kinetic frictional forces exist when one object slides across another

Static frictional forces are greater than kinetic frictional forces

Coefficient of Friction

The maximum amount of frictional force that can exist between two surfaces is related to the weight of the object and the properties of the surfaces

We use the coefficient of friction (μ) to describe interaction of the two surfaces

Typically you will be given a static and kinetic coefficient depending on the situation

Normal Force

The normal force is the force that opposes the gravitational force (weight)

Currently your weight is pushing down on the chair you are sitting on and the chair is pushing back with a force that is equal and opposite

Similarly, you and the chair are applying a force on the floor and the floor is applying an equal and opposite force on you and the chair

Normal Force

In most situations, the normal force will simply be the opposite of the weight

gmF

FF

N

gN

Direction and the Frictional Force

The direction of the frictional force will not be determined from the equation

Instead, you need to look at your diagram and apply the correct direction (positive or negative) to the force

The direction will always be the opposite of the direction of motion

Frictional Force

The frictional force is the product of the normal force and the coefficient of friction

Common coefficients of friction are available in Table 4-2, p. 97

Nf FF

Uniform Motion

Normally, when an object is in a state of uniform motion, the applied force is equal to the kinetic frictional force

Additionally, when a force is applied to an object, the force that is applied just before it begins to move is assumed to be equal to the static frictional force

Net Force

Physics 11

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

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

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

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 if Physics 11, the forces we consider will be parallel or perpendicular

An Example

A 25kg crate is slid from rest across a floor with an applied force 72N applied force. If the coefficient of kinetic friction is .27, determine: 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

Springs and Hooke’s Law

Physics 11

Springs

A mass-spring system is given below. As mass is added to the end of the spring, how would you expect distance the spring stretches to change?

Springs

mgFg

gmFg 1

gmFg 2

gmFg 3

x x

x

x

springg FF

springF

Springs

2 times the mass results in a 2 times of the displacement from the equilibrium point…

3 time the mass… 3 times the displacement…

springg FF kxFspring

xkgm

kxmg

22

Hooke’s Law

Fspring: Applied force

X : displacement of the spring from the equilibrium position

K: the spring constant

kxFspring

Hooke’s Law

the restoring force is opposite the applied force. (negative sign)

Gravity applied in the negative direction, the restoring force is in the positive direction

kxFspring