Unit 5 Forces I- Newton�s First & Second Law

• Unit is the NEWTON(N)

• Is by definition a push or a pull

• Does force need a Physical contact?

• Can exist during physical contact(Tension, Friction, Applied Force)

• Can exist with NO physical contact, called FIELD FORCES ( gravitational, electric, etc)

INERTIA – a quantity of matter, also called MASS. Italian for �LAZY�. Unit for MASS = kilogram.

Weight or Force due to Gravity is how your MASS is effected by gravity.

mgW =What is the weight of an 85.3-kg person on earth? On Mars=3.2 m/s/s)?

NWNWmgW

MARS 96.272)2.3)(3.85(94.835)8.9)(3.85(

====®=

An object in motion remains in motion in a straight line and at a constant speed OR an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) Force.

There are TWO conditions here and one constraint.

Condition #1 – The object CAN move but must be at a CONSTANT SPEEDCondition #2 – The object is at REST

Constraint – As long as the forces are BALANCED!!!!! And if all the forces are balanced the SUM of all the forces is ZERO.

The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out).

å =®= 00 Facc

Some Forces

1. Gravitational Force

1. Weight

(= Gravitation Force)

A gravitational force on a body is a certain type of

pull that is directed toward a second body. Like

earth pulling us all towards it’s center.

Do we pull the earth too towards us?

The weight W of a body is the magnitude

of the net force required to prevent the

body from falling freely, as measured by

someone on the ground. For example, to

keep a ball at rest in your hand while you

stand on the ground, you must provide an

upward force to balance the gravitational

force on the ball from Earth.

3. Normal Force

4. Frictional Force

5. Tension

When a body presses against a surface, the surface (even a seemingly rigid one) deforms and pushes on the body with a normal force that is perpendicular to the surface.

If we either slide or attempt to slide a body over a surface, the motion is resisted by a bonding between the body and the surface.

When a cord (or a rope, cable, or other such object) is attached to a body and pulled taut, the cord pulls on the body with a force directed away from the body and along the cord.

A pictorial representation of forces complete with labels.

m1g

•Weight(mg) – Always drawn

from the center, straight down

•Force Normal(FN) – A surface force always drawn

perpendicular to a surface.

•Tension(T or FT) – force in

ropes and always drawn

AWAY from object.

•Friction(Ff)- Always drawn

opposing the motion.

m2g

T

TFN

Ff

1. Isolate the Object for which you are drawing the FBD

2. Represent it as a circle or square

3.. You will only show Forces acting on it§ Contact forces – Any force that is because of

objects touching it§ Non-contact force – there in only one – Mg

4. Only full Forces – NO components

5. Length of the Forces should indicate relative magnitude

Since the Fnet = 0, a system moving at a constant speed or at restMUST be at EQUILIBRIUM.

TIPS for solving problems

• Draw a FBD

• Resolve anything into COMPONENTS

• Write equations of equilibrium

• Solve for unknowns

mg

FNFf

A 10-kg box is being pulled across the table to the right at a constant speed with a force of 50N.

a) Calculate the Force of Friction

b) Calculate the Force Normal

mg

FNFa

Ff

NFF fa 50==

NFmg n 98)8.9)(10( ===

Suppose the same box is now pulled at an angle of 30 degrees above the horizontal.

a)Calculate the Force of Friction

b)Calculate the Force Normal

mg

FN Fa

Ff 30

NFFNFF

axf

aax

3.433.4330cos50cos

===== q

Fax

Fay

NFFmgFmgFF

mgF

N

ayN

ayN

N

73

30sin50)8.9)(10(

!

=

-®-=

=+¹

NORMAL FORCES

Sketch free-body diagrams for the following situations:(a) a book rests on a table; (b) you exert a downward force on thebook as it sits on the table; (c) you tie a helium-filled balloon tothe book, which remains on the table.

When does one object lose contact with another? For instance, how many helium balloons would we have to tie to the book to make it lift off the table?

Objects lose contact when the normal force between them goes to zero. The minimum number of balloons is the number needed to reduce the normal force the table exerts on the book (and the normal force the bookexerts on the table) to zero.

a. Draw FBD of this System

Isolate and Conqueryou will draw FBD of each part in a system i.e. Box1 and Box 2 separately.

If Box 1 = 20 N and Box 2= 10N

Calculate the normal force (b) exerted on box 2 by box 1, (c) exerted on box 1 by box 2, and(d) exerted on box 1 by the floor.

q In figure shown below, is the magnitude of the normal force FNgreater than, less than, or equal to mg if the block and table are in an elevator moving upward

(a) at constant speed

(a) For constant speed

Fnet=0= FN – mg=0

FN = mg

Checkpoint

Tension

Remember -We apply NFL when the object OR every part of a system is at rest or constant motion.

If this system is either in rest or in constant velocity meansAcceleration ( of the weight and of the hand) = 0

1) Draw the FBD of the 1) Object 2) hand when at Static Equilibrium

1) Draw FBD of the Pulley in (c)

1) Draw the Free body diagram for m1 and m2 2) If the system as a whole is moving with constant speed,what is the frictional force associated with m2?Assume Frictional force is directly proportional to the Mass.

Considering Systems as a whole or Subsystems will lead to the same result

60 N

Which of the Pulley systems will make your life easier ?

Mechanical Advantage = Load / Effort

What is the value of the missing mass if the system is in static equilibrium a.k.a at rest and m = 10Kg ?

If an object is NOT at rest or moving at a constant speed, that means the FORCES are UNBALANCED. One force(s) in a certain direction over power the others.

THE OBJECT WILL THEN ACCELERATE.

The acceleration of an object is directly proportional to the NET FORCE and inversely proportional to the mass.

maFmFa

maFa

NETNET

NET

=®=

1aa å= FFNETTips:1. Draw an FBD2. Resolve vectors into components3. Write equations of motion by adding and

subtracting vectors to find the NET FORCE. Always write larger force – smaller force.

4. Solve for any unknowns

A 10-kg box is being pulled across the table to the right by a rope with an applied force of 50N. Calculate the acceleration of the box if a 12 N frictional force acts upon it.

mg

FNFa

Ff

2/8.3101250smaamaFF

maF

fa

Net

=

=-

=-=

In which direction, is this object accelerating?

The X direction!

So N.S.L. is worked out using the forces in the �x� direction only

q In figure shown below, is the magnitude of the normal force FNgreater than, less than, or equal to mg if the block and table are in an elevator moving upward

(b) at increasing speed(b) For increasing speed

Fnet=ma= FN – mg

FN = ma + mg

FN > mg

Checkpoint

m1g

m2g

T

TFN

A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable.

amTamTgm

maFNet

1

22

==-

=

2

21

2

122

122

212

/7.714

)8.9)(11()(

smmmgma

mmagmamamgmamamgm

=®+

=

+=+==-

Free Body Diagram

Remember to include • Isolate the body in consideration• Draw the body• External Forces

Do not include• Other bodies• Forces exerted by the body• Internal Forces

Where does the calculus fit in?

dtxd

mdtdv

mamF2

===!!

There could be situations where you are given a displacement function or velocity function. The derivative will need to be taken once or twice in order to get the acceleration.

Example:

220.03)( tttv +=

=+=

+=+

==

)4(40.03)4(

40.03)20.03( 2

a

tdt

ttddtdva

You are standing on a bathroom scale in an elevator in a tall building. Your mass is 72-kg. The elevator starts from rest and travels upward with a speed that varies with time according to:

When t = 4.0s , what is the reading on the bathroom scale (a.k.a. Force Normal)?

4.6 m/s/s

=+=+=®=-

=

)6.4)(72()8.9)(72(N

NN

net

FmgmaFmamgF

maF

1036.8 N

Apparent weight

Rem: • Treat the x-direction and y direction

quantities separately

• Be careful with sign conventions. If you considered ‘a’ positive for a certain body , any other body pulled by it will have the same acceleration and sign

Parts A, B, and C of Fig. show three

situations in which one or two forces act on a puck that moves over

frictionless ice along an x axis, in one-dimensional motion. The puck's mass is

m = 0.20 kg. Forces F1 and F2 are

directed along the axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N.

Force F3 is directed at angle θ = 30�

and has magnitude F3 = 1.0 N. In each situation, what is the acceleration of the

puck?

Newton's Third Law: When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.

N.T. L

FBT = - FTB

FBT = FTB

; Opposite in directionEqual in Mag

On Earth In SpaceF on man by wall Ffriction on man by ground

F on man by wall

F on wall by man

Suppose that the cantaloupe and table are in an elevator cab that begins to accelerate upward.

(a) Do the magnitudes of FTC and FCT increase, decrease, or stay the same?

(b) Are those two forces still equal in magnitude and opposite in direction?

(c) Do the magnitudes of FCE and FEC increase, decrease, or stay the same?

(d) Are those two forces still equal in magnitude and opposite in direction?

2 Masses are stacked insidean elevator as shown. The elevator starts to speed downwards with an acceleration of 2 m/s2.Find Magnitude and direction of all the contact forces on 20 Kg and 30 Kg a

= 2.

00 m

/s2

ELEVATOR

20 Kg

30 Kg