Ch'4 Forces And Newtons Laws

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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
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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?

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• 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 ?
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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.

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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

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or

• Only two factors determine the acceleration---Forc
  e and Mass
• Force Units Newton (N) kg. m/s2
• What is 1 Newton ?

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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)
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Units for Mass, Acceleration Force
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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 ?)

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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
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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
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Resultant Force And Acceleration
Resultant
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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

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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
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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 ?

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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
?
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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

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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
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Weight Of An Object

• Mass m on the surface of the earth

Radius of earth Re Distance Re (approx)
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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
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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)
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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)
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What happens if I push or pull on the block ?
What happens to the normal force if the rope has
a pull 15N?
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Balancing Act
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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
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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
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Elevator Accelerating Down With a
FN mg ma ( if downward a negative) FN
mg ma
What if a -g ?
FN0
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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
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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?
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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
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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
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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
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Tension
Mass-less and non-stretch rope Force gets applied
to the box undiminished.
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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)

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Replacing The Engine
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Setting W3150N, T2582N
T13.30103N
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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)
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Non-equilibrium Applications

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

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Towing A Super Tanker
ax2.010-3
D75.0103N, m1.50108N, R40.0103N
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ax2.010-3
1.53105N
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Hauling A Trailer
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The Motion Of A Water Skier
What is the net force on skier in each picture?
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(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.
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(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.
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(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.
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(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.
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Hauling A Crate
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or
1.68m/s2
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Accelerating Blocks
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Hoisting A Scaffold
m155 kg, T540 N
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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)
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Velocity, Acceleration And Newtons Second Law Of
Motion
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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.
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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.
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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

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

Fma1 2Fma2 2a1a2
F/ma1
Fma
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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
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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

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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