CHAPTER 4 The Laws of Motion

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CHAPTER 4The Laws of Motion
Newtons First Law An object at rest remains
at rest and an object in motion continues in
motion with constant velocity (constant speed
in straight line) unless acted on by a net
external force.
in motion or at rest with respect
to the chosen frame of reference net force
vector sum of all the external forces acting on
the object FNet,x and FNet,y
calculated separately Forces Contact
Forces Applied Forces (push or pull) Normal
Force (supporting force) Frictional Force
(opposes motion) Field Forces Gravitational
Magnetic Electrostatic The typical four
forces analyzed in our study of classical
mechanics
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Newtons Second Law The acceleration of an
object is directly proportional to the net
force acting on it FNet ma

• Mass The measurement of inertia (inertial
  mass)
• Inertia The tendency of an object to resist any
  attempt to change its motion
• Book Example
• Strike golf ball w/golf club
• Strike bowling ball w/golf club
• Which has greatest inertia?
• Which has greatest mass?

Dimensional Analysis F ma kg x m/s2
newton N
1 newton 1 kg m/s2
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Weight and the Gravitational Force
Mass an amount of matter (gravitational
mass) Your mass on the Moon equals your mass
on Earth. Weight the magnitude of the force of
gravity acting on an amount of matter
F ma Fg mg w mg
NOTE Your text treats weight (w) as a scalar
rather than as a vector.
Example Your mass is 80kg. What is your
weight? w 80kg 9.8m/s2 w 780
kgm/s2 w 780 N
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Newtons Third Law If two objects interact, the
force exerted on object 1 by object 2 is
equal in magnitude but opposite in
direction to the force exerted on object 2
by object 1
Book pushes down on table with force of
9.8.N Table pushes up on book with force of
9.8.N Net Force on book 9.8N 9.8N 0N Hence,
book does not accelerate up or down.
Earth pulls on Moon equal to the force the Moon
pulls on Earth.
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Problem Solving Strategy

• Remember We are working now with only 4 forces.
• Applied Force Fa
• Normal Force FN
• Frictional Force Ff
• Gravitational Force Fg

Draw a Sketch
Determine the Magnitude of Forces in x and in
y Direction FN often equals Fg (object does
not accelerate up off surface or accelerate
downward through surface) FNet,y FN Fg 0
N FNet,x Fa Ff ma Ff lt Fa
Label forces on Sketch Solve Problem
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Example 1 Sliding Box Problem (Horizontal
Fa) Box hockey puck shopping
cart tire dead cat etc. A 55 kg
shopping cart is pulled horizontally with a force
of 25N. The frictional force opposing the motion
is 15N. How fast does the cart accelerate?
Fa 25N Ff 15N FNet,x 25N 15N ma
10.N 55kga
Fg mg 55kg 9.8m/s2 540N FN Fg 540N
a .18m/s2
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Example 2 Sliding Box Problem (Pulled at an
Angle) A dead cat with a mass of 7.5kg is pulled
off the road by a passing motorist. The motorist
pulls the cat by its tail which is at an angle of
37 to the horizontal. A force of 25N is applied.
The force of friction opposing motion is 18N. How
fast does the cat accelerate?
25N
59N
18N
74N
m 7.5kg Fa 25N
Fa,x Fa cos37 20.N Fa,y Fa sin 37 15N
FN Fa,y Fg (up forces equal down forces) Fg
mg 74N FN 74N 15N FN 59N
Ff 18N FNet,x Fa,x Ff ma 20.N 18N
7.5kg a
a .27m/s2
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Friction
Friction opposes motion. Kinetic Friction opposes
motion of a moving object. Static Friction
opposes motion of a stationary object. Ff ?FN
?static coefficient of static
friction ?kinetic coefficient of kinetic
friction
?s gt ?k
Why? Static condition peaks and valleys of the
two surfaces overlap each other. Kinetic
Condition surfaces slide over each other
touching only at their peaks
?s gt ?k ?Ff,s gt Ff,k Applied Physics
Example Anti-lock Brakes
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Example 3 Sliding Box (Pulled at Angle
advanced) A box is pulled at a 37 angle with
increasingly applied force. The box which has a
mass of 15kg begins to move when the applied
force reaches 50.N. What is the coefficient of
static friction between the box and the surface?
Fa Fa,x Fa,y Fg FN Fa,y Fg FN 120N
50.N Fa cos 37 40.N Fa sin 37 30.N mg
150N
Fa,x
Ff,s At the point where box started to
move Ff,s ?s FN Fa,x ?s 120N 40N
?s .33
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Forces on an Inclined Plane
Fg is always directed straight down. We then
choose a Frame of Reference where the x-axis is
parallel to the incline and the y-axis
perpendicular to the incline. Fg,x Fg
sin? Fg,y Fg cos? FN Fg,y (in opposite
direction) Fa and Ff will be along our new x-axis
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Example Problem (Inclined Plane) A 25.0kg box is
being pulled up a 30 incline with a force of
245N. The coefficient of kinetic friction between
the box and the surface is .567. Calculate the
acceleration of the box.
Draw a Sketch
Determine the Magnitude of the forces in x and y
directions
25.0 kg
m Fg Fg,x Fg,y
245N (to right along x-axis)
Fa FN Ff
mg 25.0kg 9.80m/s2 245N (down)
Fg cos? 212N (up along y-axis)
Fg sin? 245N sin30 123N (to left along
x-axis)
?kFN .567 212N 120N (to left
along x-axis)
Fg cos? 245N cos30 212N (down along
y-axis)
Label Forces on your sketch Solve the Problem
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Solve the Problem Fa Ff Fg,x
245N 120.N 123N 2N FNet,x max 2N
25.0kg ax
FNet,x
ax .08 m/s2
NOTE The box may be moving up the incline at any
velocity. However, at the specified conditions it
will be accelerating.
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Example Problem (Connected Objects Flat Surface)
Two similar objects are pulled across a
horizontal surface at constant velocity. The
required Fa is 350.N. The mass of the leading
object is 125kg while the mass of the trailing
object is 55kg. The values for ?k are the same
for each object. Calculate ?k and calculate the
Force of Tension in the connecting rope.
NOTE FT Force of Tension is not a new type of
force. It is just a specific type of applied
force.

• Label the forces.
• Calculate the magnitude of the forces.
• Solve the problem(s).

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Fg,1 Fg,2 FN,1 FN,2 Ff,1 Ff,2
FNet,x Fa
m1g 125kg 9.80m/s2 1230N (down) m2g
55kg 9.80m/s2 540N (down) 1230N
(up) 540N (up) ?k 1230N (left) ?k 540N
(left) 0N Constant Velocity a 0m/s2
ma Ff,1 Ff,2 ?k 1230N ?k 540N
?k .20
Fa 350.N ?k (1230N 540N)
FT
FT 110N
?k 540N
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m1g 25.0kg 9.80m/s2 245N (down on
right) m2g 18.0kg 9.80m/s2 176N
(down on left) 245N 176N 69N (down on right)
Fg,1 Fg,2 Fg,net
69N ma (m1 m2) a 69N (25.0kg 18.0kg)
a