Download AP Physics 1 * Unit 2

AP Physics 1 –
DYNAMICS OF FORCE AND MOTION
NEWTON’S THIRD LAW & MORE FRICTION! (IT ’S BACK!)
Newton’s Laws
CONTINUED – THE THIRD LAW & MORE ON FRICTION FORCES
Learning Objectives:
BIG IDEA 1: Objects and systems have properties such as mass and charge. Systems
may have internal structure.1.C.1.1: I can design an experiment for collecting data
to determine the relationship between the net force exerted on an object its
inertial mass and its acceleration.
[SP 4.2]
1.C.3.1: I can design a plan for collecting data to measure gravitational mass and to
measure inertial mass and to distinguish between the two experiments. [SP 4.2]
BIG IDEA 2: Fields existing in space can be used to explain interactions.
2.B.1.1: I can calculate the gravitational force on an object with mass m in a
gravitational field of strength g in the context of the effects of a net force on objects
and systems. [SP 2.2, 7.2]
Learning Objectives
BIG IDEA 3: The interactions of an object with other objects can be described by forces.
3.A.2.1: I can represent forces in diagrams or mathematically using appropriately labeled vectors with
magnitude, direction, and units during the analysis of a situation.
[SP 1.1]
3.A.3.1: I can analyze a scenario and make claims (develop arguments, justify assertions) about the forces
exerted on an object by other objects for different types of forces or components of forces. [SP 6.4, 7.2]
3.A.3.2: I can challenge a claim that an object can exert a force on itself. [SP 6.1]
3.A.3.3: I can describe a force as an interaction between two objects and identify both objects for any force. [SP
1.4]
3.A.4.1: I can construct explanations of physical situations involving the interaction of bodies using Newton’s
third law and the representation of action-reaction pairs
of forces. [SP 1.4, 6.2]
3.A.4.2: I can use Newton’s third law to make claims and predictions about the action-reaction pairs of forces
when two objects interact. [SP 6.4, 7.2]
3.B.1.1: I can predict the motion of an object subject to forces exerted by several objects using an application of
Newton’s second law in a variety of physical situations with acceleration in one dimension. [SP 6.4, 7.2]
Learning Objectives
3.B.1.2: I can design a plan to collect and analyze data for motion (static, constant, or accelerating) from
force measurements and carry out an analysis to determine the relationship between the net force and
the vector sum of the individual forces. [SP 4.2, 5.1]
3.B.1.3: I can reexpress a free-body diagram representation into a mathematical representation and solve
the mathematical representation for the acceleration of the object. [SP 1.5, 2.2]
3.B.2.1: I can create and use free-body diagrams to analyze physical situations to solve problems with
motion qualitatively and quantitatively. [SP 1.1, 1.4, 2.2]
3.C.4.1: I can make claims about various contact forces between objects based on the microscopic cause
of those forces. [SP 6.1]
3.C.4.2: I can explain contact forces (tension, friction, normal, spring) as arising from interatomic electric
forces and that they therefore have certain directions. [SP 6.2]
Learning Objectives
BIG IDEA 4: Interactions between systems can result in changes in those systems.
4.A.1.1: I can use representations of the center of mass of an isolated two-object system to analyze the
motion of the system qualitatively and semi-quantitatively. [SP 1.2, 1.4, 2.3, 6.4]
4.A.2.1: I can make predictions about the motion of a system based on the fact that acceleration is equal to
the change in velocity per unit time, and velocity is equal to the change in position per unit time. [SP 6.4]
4.A.2.2: I can evaluate using given data whether all the forces on a system or whether all the parts of a
system have been identified. [SP 5.3]
4.A.2.3: I can create mathematical models and analyze graphical relationships for acceleration, velocity, and
position of the center of mass of a system and use them to calculate properties of the motion of the center
of mass of a system. [SP 1.4, 2.2]
4.A.3.1: I can apply Newton’s second law to systems to calculate the change in the center-of-mass velocity
when an external force is exerted on the system. [SP 2.2]
4.A.3.2: I can use visual or mathematical representations of the forces between objects in a system to
predict whether or not there will be a change in the center-of-mass velocity of that system. [SP 1.4]
Topic: Newton’s Third Law
Essential Questions:
What is the third law and how does it relate to our interaction with objects and surfaces?
rd
Newton’s 3
Law
“For every action there is an EQUAL and OPPOSITE
reaction.
◦ This law focuses on action/reaction pairs (forces)
◦ They NEVER cancel out
All you do is SWITCH the wording!
•PERSON on WALL
•WALL on PERSON
rd
Newton’s 3
Law
This figure shows the force during a collision
between a truck and a train. You can clearly
see the forces are EQUAL and OPPOSITE. To
help you understand the law better, look at
this situation from the point of view of
Newton’s Second Law.
FTruck  FTrain
mTruck ATruck  M TrainaTrain
There is a balance between the mass and acceleration. One object usually has a
LARGE MASS and a SMALL ACCELERATION, while the other has a SMALL MASS
(comparatively) and a LARGE ACCELERATION.
Examples:
Action: HAMMER HITS NAIL
Reaction: NAIL HITS HAMMER
Action: Earth pulls on YOU
Reaction: YOU pull on the earth
Summary for
rd
Newton’s 3
Law
Take a moment to write your two sentence summary that reflects on the preceding information.
Friction
KINETIC AND STATIC
(YES, IT ’S ALL ABOUT THE FRICTION FORCES AGAIN!)
Topic: Friction Forces
ESSENTIAL QUESTIONS:
WHAT IS FRICTION EXACTLY?
HOW DO SURFACES INTERACT?
HOW DO WE SOLVE FOR THE COEFFICIENT OF FRICTION?
Types of Friction
Static – Friction that keeps an object at rest and prevents it from moving
Kinetic – Friction that acts during motion
Force of Friction
F f  FN
The Force of Friction is
directly related to the Force   constant of proportion ality
Normal.
  coefficien t of friction
◦ Mostly due to the fact that BOTH
are surface forces
Fsf   s FN
The coefficient of
Fkf   k FN
friction is a unitless
constant that is
specific to the
material type and
usually less than one.
Note: Friction ONLY depends on the MATERIALS sliding against each
other, NOT on surface area.
Example:
A 1500 N crate is being pushed across
a level floor at a constant speed by a
force F of 600 N at an angle of 20°
below the horizontal as shown in the
figure.
Fa
a) What is the coefficient of kinetic
friction between the crate and the
floor?
F f   k FN
FN
Fay
F f  Fax  Fa cos   600(cos 20)  563.82 N
FN  Fay  mg  Fa sin   1500
20
FN  600(sin 20)  1500  1705.21N
Fax
563.82   k 1705.21
 k  0.331
Ff
mg
Example:
If the 600 N force is instead pulling the block
at an angle of 20° above the horizontal as
shown in the figure, what will be the
acceleration of the crate. Assume that the
coefficient of friction is the same as found in
(a)
FN
20
Fax
FNet  ma
Fax  F f  ma
Fa cos   FN  ma
Fa cos    (mg  Fa sin  )  ma
600 cos 20  0.331(1500  600 sin 20)  153.1a
563.8  428.57  153.1a
a  0.883 m / s 2
Fa
𝐹𝑓
mg
Fay
Inclines

Ff
FN




mg
mg sin 

Tips
•Rotate Axis
•Break weight into components
•Write equations of motion or
equilibrium
•Solve
Example:
Masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes over a
frictionless pulley. As shown in the diagram, m1 is held at rest on the floor and m2 rests on a fixed
incline of angle 40 degrees. The masses are released from rest, and m2 slides 1.00 m down the
incline in 4 seconds. Determine (a) The acceleration of each mass (b) The coefficient of kinetic
friction and (c) the tension in the string.
T
FN
Ff
m2gcos40
m2g
m1
40
m2gsin40
m1g
T  m1 g  m1a  T  m1a  m1 g
m2 g sin   ( F f  T )  m2 a
40
T
FNET  ma
FNET  ma
Example:
T  m1 g  m1a  T  m1a  m1 g
m2 g sin   ( F f  T )  m2 a
x  voxt  1 at 2
2
1  0  1 a ( 4) 2
2
a  0.125 m / s 2
T  4(.125)  4(9.8)  39.7 N
m2 g sin   F f  T  m2 a
m2 g sin   F f  (m1a  m1 g )  m2 a
m2 g sin    k FN  m1a  m1 g  m2 a
m2 g sin    k m2 g cos   m1a  m1 g  m2 a
m2 g sin   m1a  m1 g  m2 a   k m2 g cos 
k 
m2 g sin   m1a  m1 g  m2 a
m2 g cos 
k 
56.7  0.5  39.2  1.125
 0.235
67.57
NOW YOU TRY THESE MONSTER EQ’S!
ON YOUR OWN! SHOW YOUR WORK!
Fa
Try it On Your Own!
FN
Fay
A 1300 N crate is being pushed across a level floor at a constant speed
30
Fax
by a force F of 750 N at an angle of 30° below the horizontal as shown
in the figure (at right.)
Ff
mg
a) What is the coefficient of kinetic friction between the crate and the floor?
Show Your Work!
If the 750 N force is instead pulling the block at an angle of 30° above the horizontal as shown in
the figure, what will be the acceleration of the crate?
Assume that the coefficient of friction is the same as found in (a)
Try it On Your Own!
If the 750 N force is instead pulling the block at an angle of 30° above the horizontal as shown in
the figure, what will be the acceleration of the crate?
Assume that the coefficient of friction is the same as found in (a)
Show Your Work!
30
Fax
𝐹𝑓
mg
Fay
Try it On Your Own!
Masses m1 = 6.00 kg and m2 = 11.00 kg are connected by a light string that passes over a
frictionless pulley. As shown in the diagram, m1 is held at rest on the floor and m2 rests on a
fixed incline of angle 50 degrees. The masses are released from rest, and m2 slides 2.00 m down
the incline in 3 seconds. Determine (a) The acceleration of each mass (b) The coefficient of
kinetic friction and (c) the tension in the string.
T
FN
Ff
m2gcos40
m2g
m1
40
m2gsin40
m1g
T  m1 g  m1a  T  m1a  m1 g
m2 g sin   ( F f  T )  m2 a
50
T
FNET  ma
Try it On Your Own!
Masses m1 = 6.00 kg and m2 = 11.00 kg are connected by a light string that passes over a
frictionless pulley. As shown in the diagram, m1 is held at rest on the floor and m2 rests on a
fixed incline of angle 50 degrees. The masses are released from rest, and m2 slides 2.00 m down
the incline in 3 seconds. Determine (a) The acceleration of each mass (b) The coefficient of
kinetic friction and (c) the tension in the string.
T
FN
Ff
m2gcos40
m2g
m1
40
m2gsin40
m1g
T  m1 g  m1a  T  m1a  m1 g
m2 g sin   ( F f  T )  m2 a
50
T
FNET  ma
Example:
Masses m1 = 6.00 kg and m2 = 11.00 kg are connected by a light string that passes over a
frictionless pulley. As shown in the diagram, m1 is held at rest on the floor and m2 rests on a fixed
incline of angle 50 degrees. The masses are released from rest, and m2 slides 2.00 m down the
incline in 3 seconds. Determine (a) The acceleration of each mass (b) The coefficient of kinetic
friction and (c) the tension in the string.
T
FN
Ff
m2gcos40
m2g
m1
40
m2gsin40
m1g
T  m1 g  m1a  T  m1a  m1 g
m2 g sin   ( F f  T )  m2 a
40
T
FNET  ma
FNET  ma
Example:
T  m1 g  m1a  T  m1a  m1 g
m2 g sin   ( F f  T )  m2 a
x  vox t  1 at 2
2
2  0  1 a (3) 2
2
a  0.111 m / s 2
T  6(.111)  6(9.8)  59.47 N
m2 g sin   F f  T  m2 a
m2 g sin   F f  (m1a  m1 g )  m2 a
m2 g sin    k FN  m1a  m1 g  m2 a
m2 g sin    k m2 g cos   m1a  m1 g  m2 a
m2 g sin   m1a  m1 g  m2 a   k m2 g cos 
k 
m2 g sin   m1a  m1 g  m2 a
m2 g cos 
k 
82.57  0.66  58.8  1.221
 0.315
69.29