Newtons Second Law of MotionForce and Acceleration

1
Chapter 5

• Newtons Second Law of Motion--Force and
  Acceleration

2
Force Causes Acceleration

• In order to make an object at rest move, it must
  accelerate
• suppose you hit a hockey puck
• as it is struck it experiences acceleration, but
  as it travels off at constant velocity (assuming
  no friction) the puck is not accelerating
• if the puck is struck again, then it accelerates
  again the force the puck is hit with causes the
  acceleration
• acceleration depends on net force
• to increase accelerationincrease net force
• double accelerationdouble the force
• Force Acceleration
• directly proportional

3
Mass Resists Acceleration

• Acceleration depends on mass
• to decrease accelerationincrease mass
• to increase accelerationdecrease mass
• double the mass ½ the acceleration
• Acceleration 1/mass
• inversely proportional

4
Newtons Second Law

• Newton was the first to realize that acceleration
  produced when something is moved is determined by
  two things
• how hard or fast the object is pushed
• the mass of the object
• Newtons 2nd Law
• The acceleration of an object is directly
  proportional to the net force acting on the
  object and is inversely proportional to the
  objects mass

5
Newtons Second Law

• a F/m or F ma
• Robert and Laura are studying across from each
  other at a wide table. Laura slides a 2.2 kg
  book toward Robert. If the net force acting on
  the book is 1.6 N to the right, what is the
  books acceleration?
• A 30.0 g arrow is shot by William Tell through an
  8.00 cm thick apple sitting on the top of his
  sons head. If the arrow enters the apple at
  30.0 m/s and emerges at 25.0 m/s in the same
  direction, with what force has the apple resisted
  the arrow?

6
Newtons Second Law

• 3. An applied force of 50 N is used to
  accelerate an object to the right across a
  frictional surface. The object encounters 10 N of
  friction. Use the diagram to determine the normal
  force, the net force, the mass, and the
  acceleration of the object. (Neglect air
  resistance.)
• 4. Rose is sledding down an ice-covered hill
  inclined at an angle of 15.0 with the
  horizontal. If Rose and the sled have a combined
  mass of 54.0 kg, what is the force pulling them
  down the hill?

7
Newtons 2nd Law Kinematics

• A 4.60 kg sled is pulled across a smooth ice
  surface. The force acting on the sled is of
  magnitude 6.20 N and points in a direction 35.0
  above the horizontal. If the sled starts at
  rest, how fast is it going after being pulled for
  1.15 s?
• The fire alarm goes off, and a 97 kg fireman
  slides 3.0 m down a pole to the ground floor.
  Suppose the fireman starts from rest, slides with
  a constant acceleration, and reaches the ground
  floor in 1.2 s. What was the force exerted by
  the pole on the fireman?

8
Friction

• Acts on materials that are in contact with each
  other
• Always acts in a direction to oppose motion
• Depends on type of surfaces
• Rubber against concrete produces more friction
  than steel against steel
• Occurs in liquids and gases
• Air resistance, running in water
• When friction is present an object can still move
  at a constant velocity
• The friction force must balance outside forcenet
  force would be zero (no acceleration)

9
Friction

• Does friction act on an object at rest?
• No, there must be movement
• Suppose a biker cruises with a constant velocity
  but the thrust from his pedaling is 10 N. What
  is the acceleration of the bike?
• 0 m/s2 the bike is moving at a constant speed
• What is the force of air resistance (friction)
  acting on the bike?
• 10 N in the direction opposite the motion of the
  bike these forces must balance or the bike would
  be accelerating

10
Friction

• Types of Friction
• Static
• The resistance force that must be overcome to
  start an object in motion
• Kinetic/Sliding
• The resistance force between two surfaces already
  in motion
• Rolling
• The resistance force between a surface and a
  rolling object
• Fluid
• The resistance force between and object and a
  fluid/gas (air resistance)

11
Sliding Friction

• Ffriction µFnormal
• µ the coefficient of sliding friction (has no
  units)
• 1. Brian is walking through the school cafeteria
  but does not realize that the person in front of
  him has just spilled his glass of chocolate milk.
  As Brian, who weighs 420 N, steps in the milk,
  the coefficient of sliding friction between Brian
  and the floor is suddenly reduced to 0.040. What
  is the sliding force of friction between Brian
  and the slippery floor?

12
Friction

• While redecorating her apartment, Kelly slowly
  pushes an 82 kg china cabinet across the wooden
  dining room floor, which resists motion with a
  force of 320 N. What is the coefficient of
  sliding friction between the china cabinet and
  the floor?
• 3. A rightward force is applied to a 10-kg
  object to move it across a rough surface at
  constant velocity. The coefficient of friction,
  µ, between the object and the surface is 0.2. Use
  the diagram to determine the gravitational force,
  normal force, applied force, frictional force,
  and net force.
• (Neglect air resistance.)

13
Applying ForcePressure

• Pressure the amount of force per unit area
• P F/A
• Units are Pascals (Pa) N/m2
• Suppose you are standing on the ground. Do you
  exert more pressure when you stand on both feet
  or stand on one foot?
• The force, your weight, is the same in both
  cases. Two feet have more area than one foot,
  therefore, there will be more pressure exerted if
  you are standing on one foot.

14
Pressure

• Brooke comes home from school and puts her books
  down on the kitchen table. The books have a
  combined weight of 25 N and the area in contact
  is 0.19 m by 0.24 m. What pressure do the books
  apply on the table?
• 2. A full coffee mug has a mass of 0.60 kg and
  an empty mug has a mass of 0.30 kg. a.) Which
  mug, the full or empty one, applies a greater
  pressure on the table? b.) If the full mug
  applies a pressure of 1200 N/m2, what is the area
  of the circular ring of coffee left on the table
  by the bottom of the mug?

15
Free Fall Explained

• Do heavy objects always fall faster than light
  objects?
• Only in the presence of air resistance
• Newtons Second Law (F ma)
• Mass is only a factor in the force not in the
  acceleration
• A heavier object will strike the ground with a
  much greater force than a lighter object, but
  they will have the same acceleration and drop time

16
Falling Air Resistance

• Air resistance obviously affects the amount of
  time it takes an object to drop.
• Think of an elephant and a feather if we dropped
  both off the school, which would land first?
• Without air resistance, they land at the same
  time
• With air resistance, the elephant lands first

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Falling Air Resistance

• For the elephant
• net force is only slightly decreased by the air
  resistance because the elephant has a large
  weight (downward force)
• For the feather
• the net force is greatly decreased by the air
  resistance because the feather has a small weight
  (downward force)

18
Falling Air Resistance

• Does the elephant or the feather experience a
  greater force due to air resistance?
• Air resistance of a falling body depends on
• How big the body is
• How fast the body is falling
• Air resistance is the result of an object plowing
  through a layer of air and colliding with air
  molecules.
• The more air molecules which an object collides
  with, the greater the air resistance force.
  Subsequently, the amount of air resistance is
  dependent upon the speed of the falling object
  and the surface area of the falling object.
• Based on surface area alone, it is safe to assume
  that (for the same speed) the ELEPHANT would
  encounter more air resistance than the feather.

19
Falling Air Resistance

• Why does the elephant fall faster if it
  experiences more air resistance than the feather?
• Objects accelerate when forces are unbalanced
• The feather has a smaller force of gravity,
  therefore its air resistance (even though it is
  smaller than the elephants) equals its force of
  gravity much faster than for the elephant.
• When these forces are equal, the feather has
  stopped accelerating and therefore reached its
  terminal speed.

20
Falling Air Resistance

• Terminal Speed the speed reached when the
  acceleration stops
• Terminal Velocity the terminal speed with its
  direction
• Ping pong ball 9 m/s baseball 20 m/s
• When the force of air resistance of a falling
  object is equal to the objects weight, what will
  the net force be?
• What will the acceleration be?
• Does this mean that the object stops falling?

21
Falling Air Resistance

• With air resistance, Newtons Second Law becomes
• a Fnet/m (weight air resistance)/m
• a (mg R)/m g R/m
• R resistance force

22
Falling Air Resistance

• A skydiver jumps. As she falls faster through
  the air, does air resistance increase, decrease,
  or remain the same?
• Does net force increase or decrease?
• As she falls faster and faster does her
  acceleration increase, decrease, or remain the
  same?
• How can a skydiver control his/her velocity?

23
Falling Air Resistance

• For each case, use the diagram to find the net
  force and the acceleration of the skydiver.