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Ch.4 Forces And Newtons Laws

What is a Force? A Push or a Pull

Two types of forces Contact and Non contact

Non Contact - Action at a distant force

Is the Force a Vector or a Scalar ? Units and

Dimensions ?

Mass Measure of Mass is inertia

(How does it differ from Weight ?) Higher mass

harder to change the motion, i.e. higher inertia

Newtons First Law Of Motion

- An object continues in a state of rest or in a

state of motion at a constant speed along a

straight line unless compelled to change that

state by a net force. - What is the net force?
- If so, why will a ball rolling on a flat

surface stop?

- Vector sum of all the forces acting on the object

is called the net force. - ( i.e. both magnitude and direction needs to be

considered)

What is the net force on the car ?

Inertial Reference Frame

- Newtons laws are valid in an inertial frame,

i.e. the acceleration of the frame should be

zero (Constant Velocity). - Ideally we do not have such a frame, but earth is

a very good approximation.

Newtons Second Law

- First law no net force no change in

velocity - Second law What happens if there is an external

force? (net)

Acceleration of the object

Net Force

Acceleration inversely proportional to mass

or

- Only two factors determine the acceleration---Forc

e and Mass - Force Units Newton (N) kg. m/s2
- What is 1 Newton ?

Newtons Second Law Of Motion

When a net external force acts on an

object of mass m, the acceleration a results is

directly proportional to the net force and has a

magnitude that is inversely proportional to the

mass. The direction of the acceleration is the

same as the direction of the net force.

SI Unit of Force kg.m/s2 newton (N)

Units for Mass, Acceleration Force

Example 1. Pushing A Car

- Frictional force 560 N
- Push 275 N 395 N 670

N - Net force 670 N 560 N, N

110 N - F ma , 110 N

1850 kga - a 110 N/1850 kg

0.059 m/s2 - (what is the direction ?)

Forces In 2-D

- Fx max
- Fy may

Two forces are applied onto an object. 1.) 12N

towards North, and 2.) 5N towards East, what is

the direction of the motion of the object?

Resultant force

tan ? 12/5 2.4 ? tan-1(12/5) 67.38 0

Example 2.

1300 kg raft P Force by the man

In 65 seconds, where will the boat be if v0x

0.15 m/s ?

(a)

A Force of wind

Resultant Force And Acceleration

Resultant

Displacement Of The Boat In 65 sec

For x v0x 0.15 m/s, ax 0.018 m/s2

t 65 sec,

x ?

x v0x t (½)axt2 0.1565

(1/2)0.018(65)2 48 m

For y v0y 0, ay 0.011 m/s2, t 65

sec

- y v0yt (½) ay t2
- 065 (½)0.011(65)2 23 m

Which of these will cause the acceleration to be

doubled ?

- a) All of the forces acting on the object

doubles - b) The net force acting on the object doubles
- c) Both the net force and the mass doubles
- d) The mass of the object is reduced by a

factor of two.

a, b, d

Newtons Third Law of Motion

- Whenever one body exerts a force on a second

body, the second body will exert an oppositely

directed force of equal magnitude on the body. - (Action reaction law)
- Acting on which object ?

MS 11000 kg

mA 92 kg

Force by Astronaut on Space Ship P Force on

Astronaut by Space ship P

What will be the acceleration of the two objects

?

Types Of Forces

- Fundamental Forces
- Gravitational force
- Strong Nuclear
- Electroweak Electromagnetic force
- All other forces are Non Fundamental
- (can be explained by a fundamental force)
- Maxwell, Unification theory

Gravitational Force

- Newtons law of Universal gravitation

r center to center

G 6.673 x 10 11 N m2/kg2

Always attractive , Planetary motion, Satellites

Weight Of An Object

- Mass m on the surface of the earth

Radius of earth Re Distance Re (approx)

Hubble Telescope

- The mass of Hubble telescope is 11600 kg.

(Re 6.38106 m, Me 5.981024 kg) - (i) What is the weight when resting on earth

surface,

- (ii) and in orbit 598 km above

(r Re 598 km)

R6.38106m598103m6.98106m

Check Your Understanding 2

m2gtm1, and the net gravitational force acting on

the third object is zero. Which of the drawings

correctly represents the locations of the object?

(d)

The Normal Force Newtons 3rd Law

Table exert a force on the block FN

Net Force on the block FN W

Normal Force The force component that a surface

exerts on the object (Normal to the contact

surface)

How can the table exert a force ? (Consider the

springs in a mattress)

What happens if I push or pull on the block ?

What happens to the normal force if the rope has

a pull 15N?

Balancing Act

Apparent Weight

- How do you feel when the elevator suddenly starts

going up?

Feel heavy?

FN

FN W ma

FN Apparent weight W True weight

Elevator Accelerating Up With a

Applying 2nd law vertically upward FN W ma

FN Wma Apparent weight is larger

than the true weight (W mg) g

9.8 m/s2

Elevator Accelerating Down With a

FN mg ma ( if downward a negative) FN

mg ma

What if a -g ?

FN0

Static And Kinetic Friction

Two surfaces touching each other Contact surface

is not smooth In addition to the normal force,

there is a force parallel to the

surface FRICTIONAL FORCE

Static Friction (fs)

- As F increases, fs increases from zero up to fs

Max

- Just before motion
- fsMax µs FN

(µs Coefficient of static friction)

Units and Dimensions of µs?

Force Needed To Start The Sled

The maximum force needed to just begin to move

need to overcome the max frictional force

i.e. F fsMax µs FN µs mg

If µs 0.35, m 38 kg

fsMax 0.35 38 9.8 130 N

What happens once it just starts moving ?

Easier to move, i.e. needs force going

down i.e. fs changes to fk Kinetic

Friction

Kinetic Friction

- fk µkFN
- (µk Coefficient of kinetic

friction)

µk is usually less than µs

Example 10 Sled riding How far does the sled

go before stopping ?

µk 0.05

fk µk FN µk mg

- Net force on the sled kinetic frictional force

Acceleration

What is the meaning of the negative sign? Does

the acceleration depend on the mass ? Stopping

distance x?

v2 v02 2ax

Tension

Mass-less and non-stretch rope Force gets applied

to the box undiminished.

Traction Of The Foot

- T1 and T2 keep the pulley on the foot at rest.

i.e. pulley is at equilibrium (Net Force 0) - Find the

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- T1 T2 ( Same rope)

Replacing The Engine

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Setting W3150N, T2582N

T13.30103N

Equilibrium At Constant Velocity

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Check Your Understanding 4

- Which of the following could lead to

equilibrium? - a) Three forces act on the object. The forces all

point along the same line but may have different

directions. - b) Two perpendicular forces act on the object.
- c) A single force acts on the object.
- d) In none of the situations described in (a),

(b) and (c) could the object possibly be in

equilibrium.

Answer (a)

Non-equilibrium Applications

- Non zero net force
- Net force x component, y component
- Acceleration in x direction and in y direction

Towing A Super Tanker

ax2.010-3

D75.0103N, m1.50108N, R40.0103N

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ax2.010-3

1.53105N

Hauling A Trailer

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The Motion Of A Water Skier

What is the net force on skier in each picture?

(a) The skier is floating motionless in the water.

The skier is floating motionless in the water, so

her velocity and acceleration are both zero.

Therefore, the net force acting on her is zero,

and she is in equilibrium.

(b) The skier is being pulled out of the water

and up onto the skis.

As the skier is being pulled up and out of the

water, her velocity is increasing. Thus she is

accelerating, and the net force acting on her is

not zero. The skier is not in equilibrium. The

direction of the net force is shown in the figure

above.

(c) The skier is moving at a constant speed along

a straight line.

The skier is now moving at a constant speed along

a straight line, so her velocity is constant.

Since her velocity is constant, her acceleration

is zero. Thus, the net force acting on her is

zero, and she is again in equilibrium, even

though she is moving.

(d) The skier has let go of the tow rope and is

slowing down.

After the skier lets go of the tow rope, her

speed decreases, so she is decelerating. Thus,

the net force acting on her is not zero, and she

is not in equilibrium. The direction of the net

force is shown in the figure.

Hauling A Crate

or

1.68m/s2

Accelerating Blocks

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Hoisting A Scaffold

m155 kg, T540 N

Check Your Understanding 5

Two boxes have masses m1 and m2, and m2 is

greater than m1. The boxes are being pushed

across a frictionless horizontal surface. As the

drawing shows, there are two possible

arrangements, and the pushing force is the same

in each. In which arrangement does the force that

the left box applies to the right box have a

greater magnitude, or is the magnitude the same

in both cases?

Answer (a)

Velocity, Acceleration And Newtons Second Law Of

Motion

The Importance Of Mass

?

gmoon1.60m/s2, T24N, µk0.20, mgearth88 N

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Conceptual Questions 1.

- Why do you lunge forward when a car suddenly

stops ? Pressed backward when the car suddenly

accelerates ?

REASONING AND SOLUTION When the car comes to a

sudden halt, the upper part of the body continues

forward (as predicted by Newton's first law) if

the force exerted by the lower back muscles is

not great enough to give the upper body the same

deceleration as the car. The lower portion of

the body is held in place by the force of

friction exerted by the car seat and the floor.

When the car rapidly accelerates, the upper part

of the body tries to remain at a constant

velocity (again as predicted by Newton's first

law). If the force provided by the lower back

muscles is not great enough to give the upper

body the same acceleration as the car, the upper

body appears to be pressed backward against the

seat as the car moves forward.

Conceptual Question 6.

- Father and daughter on ice pushing each

other, who has the higher acceleration ?

a.) According to Newton's third law, when they

push off against each other, the force exerted on

the father by the daughter must be equal in

magnitude and opposite in direction to the force

exerted on the daughter by the father. In other

words, both the father and the daughter

experience pushing forces of equal magnitude.

Problem

- 4) A 5.0 kg projectile accelerates from rest

to 4.0103 m/s . The net force on the projectile

is 4.9 105 N. What is the time for the

projectile to come to the speed? - F4.9105N, M5.0kg, v00,

vf4.0103

Problem

- 8)An arrow starting from rest leaves the bow with

a speed of 25.0 m/s. If the average force on the

arrow is doubled what will be the speed?

(Say mass m, travels a distance x before leaving

the bow) initial velocity v00, find velocity v1

v12 vo2 2a1x (first case) v22 vo2 2a2x

(second case)

- If the net force is doubled in case 2, i.e.

Fma1 2Fma2 2a1a2

F/ma1

Fma

Problem

- 15)A duck of mass 2.5 kg has a force of 0.1 N

due east. Water exerts a force 0.2 N 52o

south of east . Velocity of the duck is 0.11 m/s

due east. Find the displacement of the duck in

3.0s while the forces are active.

x component of force 0.1 0.2 cos 52

Rx0.2231N y component of force - 0.2 sin 52

Ry -0.1576 N

x ?

- Start

y ?

x vox t ½ ax t2 0.11 3 ½ ax 32

0.73158m

End

y voy t ½ ay t2 0 ½ ay 9 -0.28368m

Problem

20)REASONING AND SOLUTION The forces that act on

the rock are shown at the right. Newton's second

law (with the direction of motion as positive) is

Solving for the acceleration a gives