What is a Force? A force is a push or a pull causing a change in velocity or causing deformation.

What is a Force?

A force is a push or a pull causing a change in velocity or causing

deformation.

Dynamics What is dynamics? Dynamics is the study of the

relationship between force and motion.

How are contact forces different from long range forces? Contact forces - touching - example:

hand on desk

Long range forces - act at a distance - gravitational forces, electrostatic, magnetic

What is Newton’s First Law of Motion? Law of Inertia: tendency to resist

change An object at rest remains at rest, and an

object in motion remains in motion (same direction, constant speed) unless acted upon by an unbalanced force.

Forces are balanced: Equilibrium

Newton’s 1st Law - Types of Equilibrium

1. Static Equilibrium

object is at rest 2. Dynamic Equilibrium

object is moving at constant velocity

What is Newton’s Second Law of Motion? Unbalanced forces produce

acceleration **Acceleration is directly proportional to

force and inversely proportional to mass Fnet = ma

a = Fnet/m in reference table Units 1 kgm/s2 = 1 Newton

Example: An artillery shell with a mass of 5.5 kg is

fired from a gun with a velocity of 770 m/s. The barrel of the gun is 1.5 m long. Find the force on the shell.

Solution:

m = 5.5 kg

vf = 770 m/s

vi = 0 m/s

d = 1.5 m

€

F = ma

€

=5.5kg(2x105m /s2) =1.1x106N

€

v f2 = v i

2 + 2ad

€

(770m

s)2 = 2(a)(1.5m)

€

a = 2 x105 m

s2

Special Case - weight W = mg is a special case of F = ma,

where weight is the force, and gravity is the acceleration (can be written as Fg)

Example: What is the weight of a 5 kg object?

€

W = mg

€

=5kg(−9.8m

s2) = − 49N

Two Kinds of Mass 1. Gravitational mass - using a balance

- comparing the gravitational force on two objects (one has a known mass).

2. Inertial mass - using Newton’s 2nd law - find the force necessary to produce a specific acceleration for a given mass

Gravitational mass = inertial mass

Graph: Inertial mass

Slope is mass

F

a€

ΔyΔx

€

=F

a

€

=m

Free Body Diagrams Used to show forces on an object Sketch and Equations:

€

Fnet = ma What is Fnet?

Fnet is the sum of the forces acting in the direction of motion (vertical or horizontal)

€

+↑ −↓

Free Body Diagrams: Vertical

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

Lifted object

(Ftens is tension)

€

Fnet = Ftens + Fgrav

Example:A 50 Newton force is used to lift a 2 kg object. What is the acceleration of the object?

Lift

Weight

€

Fnet = ma

€

Fnet = lift + weight50 N

€

W = mg

€

=2kg(−9.8m

s2)

€

=−19.6N€

Fnet = 50N + (−19.6N)

€

Fnet = 30.4N

€

a =Fnetm

=30.4N

2kg=15.2

m

s2

Lift

Weight

€

Fnet = ma

€

9000N = lift + (−44,100N)

? N

€

W = mg

€

=4500kg(−9.8m

s2)

€

=−44,100N€

=4500kg(2m

s2) = 9000N

€

lift = −53,100N€

Fnet = lift + weight

Example:A 4500 kg helicopter accelerates upward at 2 m/s2. What lift force is exerted by the air on the propellers?

Alternate Solution to helicopter problem:

€

Fnet = ma

€

Fnet = lift + weight

€

ma = lift + weight

€

ma = lift + mg

€

lift = 4500kg[2m

s2− (−9.8

m

s2)]

€

=m(a− g)

€

lift = ma−mg

€

lift = −53,100N

What is Newton’s 3rd Law of Motion?

For every action, there’s an equal and opposite reaction. The force on one object is equal and opposite to the

force on the other. Object resting on a table: weight pushes back on table.

Table pushes back with an equal and opposite force called Normal force (FN). If no other vertical forces are present: normal force equals weight


Falling objects: what are the forces on an object falling through the air?



Object in freefall(with air resistance)

€

Fnet = Fair + Fgrav

Object in freefall(no air resistance)

€

Fnet = Fgrav

Falling Objects: What are the forces on an object falling is the

air? What happens when they are equal? Drag force (Fair) - air resistance - depends on

size/shape of the object, air density, speed. When drag force = weight, forces are

balanced (Fnet=0) No net force means no acceleration! You

have reached TERMINAL VELOCITY.

Free Body Diagrams Free body diagram - horizontal motion

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

€

Fnet = maFf

FN

FA

Fg or W

€

Fnet = FA + Ff

What if…. FA is greater than Ff

acceleration is positive FA is equal to Ff then

no acceleration (constant velocity) FA is less than Ff

acceleration is negative (you can slow down, but friction won’t make you move backwards!)

Free Body Diagrams Free body diagram - horizontal motion

with no friction:



€

Fnet = ma

€

Fnet = applied force only

Example: If you apply a 50 Newton force to a mass of 5

kg, what is the acceleration?

€

a =Fnetm

€

=50N

5kg

€

=10m

s2

Example (continued): What if a frictional force of 20 N opposes the applied

force? Find a.

€

Fnet = 50N + (−20N) = 30N

€

a =Fnetm

€

=30N

5kg

€

=6m

s2

What is friction?Friction - force opposing motion between 2

surfaces in contact and parallel to the surface How can you calculate frictional force? Equation:

€

Ff = μFNFf = frictional force (N)FN = normal force (N) coefficient of friction (no units)

What variables affect friction?

Weight? YES Surface area? NO Type of surfaces in contact? YES Velocity? NO Normal force - force pushing objects together- is

normal force always equal to weight? NO - they are not equal if other vertical forces are

present.

What are two types of friction? 1. Static - objects are NOT in relative motion

- static friction opposes the START of motion 2. Kinetic (sliding) - force between surfaces

in motion - resists motion Which is greater? Static friction is greater - it is harder to start

motion that it is to keep an object moving.

€

Fstatic > Fkinetic

Example #1: A block is place on a table. It has a weight of 50 N.

You must exert a force of 20 N to keep the block moving at a constant velocity.

1. What is coefficient of sliding friction?



€

Fg = 50N€

FA = 50N

€

FN = 50N

€

Ff = 50N

€

a = 0m

s2(FA = Ff )

€

=FfFN

€

=20N

50N

€

=0.4

2. Place a 10 N brick on the block. What force is required to keep the block moving at constant velocity?

Same surfaces, so = 0.4

€

FA = Ff = μFN

€

=0.4(60N) = 24N

Example #2 A 10kg box made of wood is pushed on

a wood floor with a force of 100 N. (a.) Will the box slide? (b.) What force must be applied to

move the box at a constant velocity? (c.) What force must be applied for the

box to accelerate at a rate of 5 m/s2?

Solution:

(a.) Will it move? It will move if the applied force exceeds the static frictional force.

€

Ffs = μFN From reference table: static = 0.42

€

FN =W = mg

€

=10kg(9.8 m /s2) = 98N

€

Ffs = μFN

€

=0.42(98N) = 41.2N

€

Is FA > Ffs ? Yes, 100N>41.2N, box will slide.

Solution: (b). To move box at a constant velocity….. Use

KINETIC friction.

From reference table: kinetic = 0.30

Since a = 0, then Fnet = ma =0

€

FA = Ffk

€

Ffk = μFN = 0.30(98N) = 29.4N

€

FA = Ffk = 29.4N

Solution:

(c.) a = 5 m/s2, find FA

€

Fnet = ma

€

=10kg(5m

s2)

€

=50N

€

So.....FA + Ffk = 50N

€

FA + 29.4N = 50N

€

FA = 20.6N

What is a Force? A force is a push or a pull causing a change in velocity or causing deformation.

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