Download Unit 2D: Laws of Motion

Name:__________________________
Regents Physics
UNIT 2D
Laws of Motion
Date:___________
Mr. Morgante
Laws of Motion
Science of Describing Motion is Kinematics.
Dynamics- the study of forces that act on bodies in motion.
First Law of Motion (Inertial Mass)
An object remains at rest or moves with uniform velocity unless it is acted upon by an unbalanced force.
[Hard to prove this on earth because of all the forces such as gravity, friction, etc. Closest thing is an airhockey table. Ex. This law holds true in space.]
This 1st Law is also called the “Law of Inertia”.
Examples: Ball on incline with and without Friction; Executive Desktoy
Friction and Inertia
This does not obey 1st Law. Why?
Ground
Block moves but eventually slows down due to FRICTION (unbalanced force)
Friction- The force that opposes the motion of one surface over another.
Ex: on Earth?
Friction Ex.
a=3.0 m/s2
1.
m=5 Kg
F=20N [On Earth]
Newton’s 2nd Law is F= ma
F= 5kg x 3m/s2 = 15N
Does the forces balance? Check it!
What is the missing force? Draw F.B.D. to find out that you are losing 5N to Friction in order for the
forces to balance out!
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FNet is equal to the NET force after you are done adding all the vectors in all directions. (If
the net force =0 the it is at equilibrium, if not it is an unbalanced force)
Ff = Force of Friction
a
15N=(Ff) 10 Kg
50N=(Fapplied)
A) Find unbalanced force
B) Find acceleration of object using FNet = ma
A) FNet = Fapplied - Ff = 50N – 15N = 35N
B) a = FNet/ m = 35N/10kg = 3.5 m/s2
Coefficient of Kinetic Friction
μK = Coeff. of Kinetic Friction [Applies to objects on Earth]


Ff (Friction Force) is directly proportional to FN (Normal Force) of an object.
FN (Normal Force) is the force that results from the surface that the object is in contact with
(a.k.a. Contact Force)
Equation is Ff = μK * FN
mu “greek” mew “phonetics”
FN = m·g = Fw
FN
Fw
Example
Ff =5N
Direction of Sliding
m=5kg
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a) What is μK?
b) Set up the FBD on your own
Ff = μK * FN Where Ff = 5N; FN = Fw = mg = 5kg *9.8 m/s2 = 49 N
Note FN = Fw here because Fw creates the contact force on the surface
Note there are NO UNITS FOR μK !!!!!!!! (Newtons/Newtons = 1)
Typical Block FBD
FN
Ff
Fpull or Fapplied
FW
Again, where FN = Normal Force; Ff = Friction Force; Fpull = force pulling or applied; Fw = Force due
to weight.
Above are the forces that occur on a block or other object that is on a HORIZONTAL SURFACE
that has a force pulling it in the horizontal direction.
Simplified Free Body Diagram (FBD) of the Diagram above
FN
Ff
Fpull
Fw
This is an FBD in its fundamental form. FBD’s are intended to only show forces and the angles
between them.
What is a Newton?
1 Newton (N) is equal to the force that a 1 kilogram (kg) mass exerts. You should be able to develop
the relationship with units to satisfy this statement based on FNet=ma.
Acceleration and Freefall
Every falling body experiences acceleration (g) which is equal to 9.81 m/s2 on the earth.
What force does a 10 kg mass fall with?
The weight of the object is the force that it falls with! F=ma or W=mg in this case since we are
talking about gravity as acceleration and is denoted as g.
4
_
+
+
Remember, sign convention is important here.
X-direction
Y-direction
What about your mass?
We can find mass of an object using FNet=ma.
From FNet=ma we can rearrange it to show FNet/a=m. If we know force and acceleration, we can get
the mass.
Gravitational mass is the mass with respect to gravity (g=9.81 m/s2)
Inertial mass is the mass with respect to acceleration applied to move an object.
F
mass
a
Newton’s 2nd Law of Motion
FNet/a = m (m is constant, your mass doesn’t change anywhere in the universe!!)
What if we apply the same force to different masses? The acceleration of that object will change, but the
mass will stay the same!!
Newton’s 2nd Law – When an unbalanced force acts upon a body, it accelerates the body in the direction
of the force. The acceleration produced is directly proportional to the force applied.
Newton’s 3rd Law of Motion
“For every action or force, there is an equal and opposite reaction or force.”
This statement is the basis for equating the normal force to the weight of an object that is on a horizontal
surface.
FN
These are both
Equal & opposite Forces!
Fw
We will use Newton’s 3rd Law extensively in the Inclined Planes Unit and other Mechanics units.
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NAME________________________________
Regents Physics
Friction Notesheet
Date________
Mr. Morgante
Define:
1. Friction:
2. Normal force:
3. Coefficient of friction:
4. Static friction:
5. Kinetic friction:
Equation
Variables/constants
Can be used to find…
Units
Ff = μFN
Algebra review
Using Ff = μFN ; solve for μ
solve for FN
Approximate Coefficients of Friction
Rubber on concrete (dry)
Rubber on asphalt(dry)
Wood on wood
Kinetic
_______
_______
_______
Static
_______
_______
_______
Free-body diagrams Label diagrams with Fg,FN,Ff, mass
Case 1
Case 2
Object on frictionless surface
F
Acceleration =__________
Case 4
Wood on wood;
Object at rest
Case 3
Wood on wood;
incline; constant
velocity
F
Acceleration =__________ Acceleration =_________
Wood on wood; object moving at constant velocity
Acceleration =__________
(OVER)
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Graphs
Friction vs. Normal Force graph
Magnitude of friction as applied force graph
Applied Force
Normal force
Applications
Rubber car tire on dry asphalt
Label diagrams with Fg,FN,Ff, mass
Rubber car tire on wet asphalt
Label diagrams with Fg,FN,Ff, mass
Velocity
Velocity
Rolling friction and Fluid friction
1. Rolling friction:_____________________________________________________
2. Fluid friction:_______________________________________________________
3. How would fluid friction affect free-fall situations?
____________________________________________________________________
Summary: Ff = _______
1.Theoretically, should frictional force depend on surface area?
_______
2. Theoretically, should frictional force depend on the speed of motion?
_______
3. Theoretically, the frictional force should depend on : __________ &
____________
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Name____________________________________
Regents Physics
Notesheet: Forces
Vocabulary- Define the Following
Date_______
Mr. Morgante
1. Dynamics:_________________________________________________________
2. Force: ____________________________________________________________
3. Resultant:__________________________________________________________
4. Equilibrant: ________________________________________________________
5. Newton’s 1st Law of Motion:__________________________________________________________
_____________________________________________________________________________________
6. inertia: _______________________________________________________________
7. mass:_________________________________________________________________
8. weight:________________________________________________________________
9. kilogram:______________________________________________________________
10.Newton's 2nd Law of Motion:__________________________________________________________
_____________________________________________________________________________________
11. Statics:____________________________________________________________________
12. Newton(unit) _______________________________________________________________
13. Newton’s Third Law of Motion:________________________________________________________
_____________________________________________________________________________________
14. Net Force: ____________________________________________________________
15. Contact Force:_________________________________________________________
16. Normal Force:_________________________________________________________
17. Static equilibrium:______________________________________________________
18. Concurrent forces:
19. Equilibrium:
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20.Free-body diagram:
Regents Physics Reference Table Review:
Use your Mechanics section to outline all equations that have an “F” term.
Equation
Variables
Units
Can be used to find:
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Name:_______________________
Regents Physics
Date:____________
Mr. Morgante
Newton’s Laws of Motion Practice
Show all work to solve the problems below.
Remember to use the correct units.
Use the following formula and values:
F = Force m = mass, a = acceleration dues to the Earth’s gravity = 9.8 m/s/s
Level I
1. What force is needed to give a mass at 50 kg an acceleration of 10 m/s/s?
2. A force of 12 N acts upon a 3 kg mass. What is the acceleration of the mass?
3. It takes a force of 25 N to give a body an acceleration of 5 m/s/s. What is the mass of the body?
4.
What is the weight C on Earth of a 100 kg piece of lead?
5.
What is the mass of an object that weighs 980N on Earth?
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Name:_______________
Regents Physics
Date_____________
Mr. Morgante
Newton’s Laws of Motion Practice 2
Level II
1.
A 10 kg rocket fired horizontally encounters a force of air resistance of 8.0 N. The force supplied
by the rocket’s engine is 70.5 N.
a) What is the net force accelerating the rocket?
b) Calculate the acceleration of the rocket.
2.
Find the gravitational force exerted on a photon at sea level whose mass is 1.7 X 10-27 kg.
3.
An electron is accelerated uniformly from rest to a speed of 4.0 x 106 m/s in 2.0 s.
a) What is the acceleration of the electron?
b) If the mass of the electron is 9.1 X 10-31 kg what is the force producing this acceleration?
(OVER)
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Rocket Scientist Level
4.
a) What is the mass of a rocket weighing 196 N?
b) What force in excess of the weight of the rocket is needed to accelerate it upward of 4.0 m/s/s.
c) What is the total force upward that must be exerted on the rocket to give it this acceleration?
5. a) What force in excess of the weight of a 500 kg rocket is needed to accelerate it upward at a rate
equal to that of gravity (9.8m/s/s)?
b) What is the total force acting on the rocket?
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Name:_____________
Mr. Morgante
Date:_________
Regents Physics
Worksheet – Newton’s Laws
1. An object with a mass of 0.5 kilogram starts from rest and achieves a maximum speed of 20
meters per second in 0.01 seconds. What average unbalanced force accelerates this object?
(1 ) 1,000 N (2 ) 10 N
(3 ) 0.1 N
(4 ) 0.001 N
2. A force of 50. newtons causes an object to accelerate at 10. meters per second squared. What is the
mass of the object?
(1 ) 500 kg (2 ) 60. kg
(3 ) 5.0 kg (4 ) 0.20 kg
3. What is the essential characteristic of an object at equilibrium.
(1 ) Zero velocity (2 ) zero acceleration
(3 ) zero potential energy (4 ) zero kinetic energy
4. Each diagram below shows a different block being pushed by a force across a surface at a constant
velocity.
In which two diagrams is the force of friction the same (Hint look at Reference Tables for )?
(1 ) A and B (2 ) B and D
(3 ) A and D (4 ) C and D
5. A bird feeder with two birds has a total mass of 2.0 kilograms and is supported by wire as shown
in the diagram on the next page.
(OVER)
The Force in the top wire is approximately
(1 ) 10. N (2 ) 14 N
(3 ) 20. N (4 ) 39 N
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6. A horizontal force is used to pull a 5.0-kilogram cart at a constant speed of 5.0 meters per second
across the floor, as shown in the diagram.
If the force of friction between the carts and the floor is 10. newtons, the magnitude of the
horizontal force along the handle of the cart is
(1 ) 5.0 N
(2 ) 10. N
(3 ) 25 N
(4 ) 50. N
7. A 60 kilogram astronaut weighs 96 newtons on the surface of the moon. The acceleration due to
gravity on the moon is
(1 ) 0.0 m/s2
(2 ) 1.6 m/s2
(3 ) 4.9 m/s2
(4 ) 9.8 m/s2
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Name:______________
Regents Physics
Date:___________
Mr. Morgante
FRICTION PROBLEMS
Questions to ask after reading the problem?
a) Is there constant speed (rest) or acceleration?
b) If there is an unbalanced force what is the acceleration?
Balanced force implies constant speed. The force due to friction can be read on the weight scale. Unbalanced force
implies acceleration?
Note:
If the question is vague but asks for the calculation of acceleration then there is an unbalanced force! ! ! !!!
Example A - Constant speed
A 1200g block is moved across a table at a constant speed. It is carrying a 350g object. The scale thats pulling the
block and the object reads 4.5N. Draw a diagram and use arrows to show the forces on the block.
a)
What is the weight of the block? The Block and the Mass?
b)
What is the Normal force?
c)
What is the force due to friction?
d)
Calculate the coefficient of friction.
e)
Suppose your calculation of the coefficient of friction were 1.85? Could this be possible?
Sketch the friction/Normal force graph for constant speed.
Sketch the coefficient of friction /Normal force graph for constant speed.
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Name____________________________________
Date_______
Regents Physics
Mr. Morgante
“Force Vector Toolkit Review”
Objective:
Review the various methods to solve force vector, free-body diagrams
Reminders: Vectors should have arrowhead, scale, use colored pencil/pen for resultant
Triangle Method of Adding Concurrent Forces
Show “head–to–tail” method
F1
P
F2
F1
P
F2
Describe steps in “head–to–tail” method: ______________________________________
Parallelogram Method of Adding Concurrent Forces
Show the steps on the concurrent vectors below:
F1
P
F2
Specific Methods to Add Vectors at Right Angles to each other
SOHCAHTOA:
R
F2
θ
Pythagorean Theorem:
F1
(over)
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Show coordinate systems!!!!
1. Two vectors, 8 N & 10 N are placed concurrently at point P.
a)Sketch ;solve the MAXIMUM resultant b) Sketch; solve the minimum resultant
+
P
+
P
2. What is the resultant of 55N in the +x direction and 75 N in the –y direction
acting at point X? Reference your resultant direction to the + x axis:
+
X
3. Can two vectors of magnitude 5N each ever have a Resultant of :
a) 7N (show sketch & angles) b) 5N (show sketch & angles) c) 4N (show sketch & angles)
d) 0 N (show sketch and angles) e) 12 N (show sketch and angles)
4. What is the equilibrant of 7 N North and 10 N South (show sketch and angles)
5. A vector of 16 N pulls at an angle of 37° to the horizontal. Show x and y comps.
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Name____________________________________
Regents Physics
Forces Algebra Review + Practice
1. If Fnet = ma , solve for:
Date_______
Mr. Morgante
m = __________ , a = ___________
2. If Fnet = ma, and a = v / t, Fnet = m v / t . Solve for:
m = ____________
, v = ___________ t = _____________
3. If Fnet = ma , and m = mass (kg) and a = acceleration (m/s2),
what are the units of Force? ___________________
4. A constant unbalanced force is applied to an object for a period of time.
Which graph best represents the acceleration of the object as a function of elapsed time?
a
a
a
t
(1)
a
t
(2)
t
(3)
t
(4)
Explain your reasoning:
5. What can the graph of FNet versus mass tell you?
FNet (N)
what type of relationship is shown?_____
What are the units of the slope?________
Mass (kg)
6. Compare and contrast the equations
a = Fnet / m
and g = Fg / m
Similarities:________________________________________________________
Differences:________________________________________________________
(OVER)
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7. Sketch and solve the following:
a. Two forces are applied to a 5.0 kg block initially at rest on a frictionless horizontal surface:
+y
F1 = 2 N
F2=10 N
+x
Calculate the sum of the horizontal forces:
______________
Calculate the acceleration of the block:
______________
Calculate the weight of the block:
______________
Show the Fg and FN vectors on the drawing: ______________
Calculate the normal force on the block:
______________
b. Two forces are applied to a 10.0 kg block initially at rest on a frictionless horizontal surface:
F2 = 25 N
+y
F1 = 5 N
+x
θ = 35°
Calculate the sum of the horizontal forces:
______________
Calculate the acceleration of the block:
______________
Calculate the weight of the block:
______________
Show the Fg and FN vectors on the drawing: ______________
Calculate the normal force on the block:
______________
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Name____________________________________
Regents Physics
Force Practice #1
Date_______
Mr. Morgante
Show all work
Solve the following:
1. Two forces are applied to a 10.0 kg block initially at rest on a frictionless horizontal surface:
F2 = 50 N
+y
F1 = 20 N
+x
θ = 35°
Magnitude
Direction
Calculate the sum of the horizontal forces:
______________
____________
Calculate the acceleration of the block:
______________
____________
Calculate the weight of the block:
______________
____________
Show the Fg and FN vectors on the drawing: Fg______________
____________
FN______________ ____________
(OVER)
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2. Scale: 1 cm = 2N.
Calculate and draw the vectors and their resultant for the following vectors acting at the origin:
+y
Vector #1
8 N (-y)
Vector #2
10 N (+x)
What angle does the resultant make with the
+x axis?_____________
+x
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Name____________________________________
Regents Physics
Newton’s 3-Laws Level 2&3
Date_______
Mr. Morgante
Show all work
Solve the following (Each problem on this page is worth one point):
1. Two forces are applied to a 8.0 kg block initially at rest on a frictionless horizontal surface:
+y
F1 = 12 N
F2=50 N
+x
Magnitude
Direction
Calculate the sum of the horizontal forces:
______________
____________
Calculate the acceleration of the block:
______________
____________
Calculate the weight of the block:
______________
____________
Show the Fg and FN vectors on the drawing: ______________
____________
Calculate the normal force on the block:
____________
______________
2. Two forces are applied to a 10.0 kg block initially at rest on a frictionless horizontal surface:
F2 = 45 N
+y
F1 = 15 N
+x
θ = 35°
Magnitude
Direction
Calculate the sum of the horizontal forces:
______________
____________
Calculate the acceleration of the block:
______________
____________
Calculate the weight of the block:
______________
____________
Show the Fg and FN vectors on the drawing: ______________
____________
Calculate the normal force on the block:
____________
______________
(OVER)
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3. A horizontal force of 70 N acts on a box of mass 15 kg
resting on a smooth, frictionless floor.
70 N
+x
(2 pts) a) Calculate the weight of the box:
a)__________
(2 pts) b) Sketch the Weight vector on the sketch above:
(2 pts) c) Calculate the Normal force on the box:
c)__________
(2 pts) d) Sketch the Normal force vector on the sketch above:
(2pts) e) Calculate the Force in the horizontal direction:
e) _________
(2 pts) f) Calculate the acceleration in the horizontal direction:
f)__________
(2 pts) g) what is the horizontal displacement of the box at t = 4.5 secs
g)_________
(OVER)
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4. The driver of a car made an emergency stop on a straight horizontal road.
The wheels locked and the car skidded to a stop. The marks made by the rubber tires
on the dry asphalt are 30 meters long and the car’s mass is 2200 kilograms.
Sketch
Known values
+x
(2 pts) a) Calculate the weight of the car:
a)_______________
(2 pts) b) Calculate the normal force exerted on the car by the road:
b)_______________
(2 pts) c) Calculate the magnitude of the frictional force the road applied to the car in stopping it.
c)_______________
(2 pts) d) If the car came to rest in 2.5 seconds, calculate the magnitude and direction of the acceleration
the car underwent.
d)______________
(2 pts) e) On the Free-body diagram below, sketch the Fg, F N, Ff vectors
+x
Z:\Physics\Regents Physics\Class Material\Unit 2D Laws of Motion 1-7-10.doc
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