Download Lesson 9 - The Link Between Force and Motion

Lesson 9 - The Link Between Force and Motion
Moving a Chair
 Try moving the chair you are sitting in. Now try moving a chair that a
person is sitting in. Which is harder?
 If you were to try to stop a rolling boulder or a rolling golf ball, which would
be easier?
 If two people pulled two kids on wagons (one 20 kg and one 40 kg) with
the same amount of force, which one would accelerate faster?
 Do you know why?
Keywords: Newton’s Second Law – Force - Mass
Introduction
So far, we have touched on:
 balanced forces
 unbalanced forces
 Newton’s First Law
A force is any kind of push or pull on an object.
Simply applying a force does not mean that an object will move.
E.g. you can push as hard as you can on a wall and never move it.
What is a balanced force?
There are two forces acting upon the book.
 One force - the Earth's gravitational
pull (Fg = the force of gravity) - exerts
a downward force.
 The other force - the push of the table
on the book (FN = normal force) pushes upward on the book.
 There is no unbalanced force acting upon the book and thus the book
maintains its state of motion.
 The book is said to be at equilibrium.
Since these two forces are of equal magnitude and in opposite directions, they
balance each other.
The general rule: when all the forces acting upon an object balance each other,
the object will be at equilibrium; it will not accelerate.
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Unbalanced Forces
When forces are unbalanced, that means there is a greater force in one
direction than in another. When there are unbalanced forces acting on an
object, this will cause the object to move in a certain direction.
Unbalanced Forces – examples
 A jet that is taking off.
Balanced & Unbalanced Forces - Check for Understanding
If the forces acting upon an object are balanced, then the object:
a. must not be moving.
b. must be moving with a constant velocity.
c. must not be accelerating.
d. none of these
Answer
 It could be A (but does not have to be A) and it could be B (but does not
have to be B).
 An object having balanced forces definitely cannot be accelerating. This
means that it could be at rest and staying at rest (one option) or could be
in motion at constant velocity (a second option).
 Either way, it definitely is not accelerating - choice C of your four choices.
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Newton’s First Law
Newton's first law of motion predicts the behavior of objects when all existing
forces are balanced.
 The first law (sometimes called the
law of inertia) states that if the
forces acting upon an object are
balanced, then the acceleration of
that object will be 0 m/s/s.
 Objects at equilibrium (the condition
in which all forces balance) will not
accelerate.
 According to Newton, an object will
only accelerate if there is an
unbalanced force acting upon it.
 The presence of an unbalanced
force will accelerate an object changing either its speed, its
direction, or both its speed and direction.
Newton’s Second Law
Newton's second law of motion predicts the behavior of objects when all
existing forces are not balanced.
 The second law states that the acceleration of an object is dependent
upon two variables
o the net force acting upon the object, and
o the mass of the object.
 As the force acting upon an object is
increased, the acceleration of the
object is increased. So, the
acceleration of an object depends
directly upon the net force acting
upon the object.
 As the mass of an object is
increased, the acceleration of the
object is decreased. So, the
acceleration of an object depends
inversely upon the mass of the object.
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Newton’s Second Law is often stated as: F = m • a
A unit of force = (a unit of mass) x (a unit of
acceleration)
By substituting standard metric units for force,
mass, and acceleration into the above
equation,
1 Newton = 1 kg • m / s2
The definition of the standard metric unit of force is stated by the above
equation:
One Newton is defined as the amount of force required to give a 1kg mass an acceleration of 1 m/s/s.
Let’s work with F = m • a
Net Force
Mass
Acceleration
(N)
10
20
20
(kg)
2
2
4
2
(m/s/s)
10
5
10
Force & Acceleration
 Comparing the values in rows 1 and 2, it can be seen that a doubling of
the net force results in a doubling of the acceleration (if mass is held
constant).
 Similarly, comparing the values in rows 2 and 4 demonstrates that a
halving of the net force results in a halving of the acceleration (if mass is
held constant).
 So, acceleration is directly proportional to net force.
Mass & Acceleration
 Observe from rows 2 and 3 that a doubling of the mass results in a
halving of the acceleration (if force is held constant).
 And similarly, rows 4 and 5 show that a halving of the mass results in a
doubling of the acceleration (if force is held constant).
 So, acceleration is inversely proportional to mass.
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Example Problems
1. A net force of 90 Newtons acts on a box which has a mass of 12 kg. What
will be the acceleration of the box?
2. A net force of 115 N is exerted on a rabbit to cause it to accelerate at a rate
of 2.55 m/s2. Determine the mass of the rabbit.
3. Suppose that a car is accelerating at a rate of 3.3 m/s2. If the net force is
tripled and the mass is halved, then what is the new acceleration of the sled?
Answer
Given:
Strategy:
Solve:
4.
a1 = 3.3 m/s2
F=m•a
a2
or
a=F/m
= 3 F / 0.5 m
=6F/m
= 6 • a1
= 6 • 3.3 m/s2
= 19.8 m/s2
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.)
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Answer
Given: Fapp = 50 N, FF = 10 N, Fg = 80 N
Goal: find the normal force, the net force, the mass, and the acceleration of the
object
Solution:
 Since there is no vertical acceleration, FN = Fg
 The Fnet is the vector sum of all the forces.
o 80 N (up) + 80 N (down) = 0 N (up-down)
o 50 N (right) + 10 N (left) = 40 N (to the right)
 To find the mass, use Fgrav = m • g (assume g = 10 m/s/s)
 So, m = Fgrav / g = 80 / 10 = 8 kg
 Find acceleration. Since, F = m • a. So, a = F / m
a = 40 / 8 = 5 m/s/s (to the right)
5.
An applied force of 20 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 coefficient of
friction ("mu") between the object and
the surface, the mass, and the
acceleration of the object. (Neglect air
resistance.)
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Answer
Given: Fapp = 20 N, FF = 10 N, Fg = 100 N
Goal: find the normal force, the net force, the mass, and the acceleration of the
object
Solve:
 Since there is no vertical acceleration, FN = Fg
 The Fnet is the vector sum of all the forces.
o 100 N (up) + 100 N (down) = 0 N (up-down)
o 20 N (right) + 10 N (left) = 10 N (to the right)
 Coefficient of friction ("mu") = Ffrict / Fnorm
 "mu" = (10 N) / (100 N) = 0.1
 To find the mass, use Fgrav = m • g (assume g = 10 m/s/s)
 So, m = Fgrav / g = 100 / 10 = 10 kg
 Find acceleration. Since, F = m • a. So, a = F / m
a = 10 / 10 = 1 m/s/s
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Newton’s Second Law - Check for Understanding
Two students are discussing their physics homework
prior to class. They are discussing an object which is
being acted upon by two individual forces (both in a
vertical direction); the free-body diagram for the particular
object is shown at the left.
During the discussion, Anna Litical suggests to Noah
Formula that the object under discussion could be
moving. In fact, Anna suggests that if friction and air
resistance could be ignored (because of their negligible size), the object could
be moving in a horizontal direction. According to Anna, an object experiencing
forces as described above could be experiencing a horizontal motion as
described below.
Noah Formula objects, arguing that the object could not have any horizontal
motion if there are only vertical forces acting upon it. Noah claims that the
object must be at rest, perhaps on a table or floor. After all, says Noah, an
object experiencing a balance of forces will be at rest.
Who do you agree with?
Answer
Anna is correct.
Noah Formula may know his formulas but he does not know (or does not
believe) Newton's laws. If the forces acting on an object are balanced and the
object is in motion, then it will continue in motion with the same velocity.
Remember
 Forces do not cause motion.
 Forces cause accelerations.
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Sci20S – Physics - Newton’s 2nd Law (F = m • a)
Name ____________________
Date ____________
1)
Explain why a person wearing a cast on one leg becomes more tired than
usual by the end of the day.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
2)
Suggest reasons why large vehicles such as vans and trucks tend to have
larger engines and higher rates of fuel consumption than smaller and more
compact cars.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
3)
Use Newton’s Laws to explain why people in a car often get neck injuries
like whiplash when struck from behind.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
4)
Explain why small rabbits can often escape bigger and faster bobcats in
pursuit by zigzagging as they run.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
5)
Predict when serious injuries are more likely to occur: when a car crashes
into a large tree or into a wooden fence.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
6)
Determine the accelerations which result when a 12-N net force is applied
to a 3-kg object and then to a 6-kg object.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
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7)
A net force of 15 N is exerted on an encyclopedia to cause it to accelerate
at a rate of 5 m/s2. Determine the mass of the encyclopedia.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
8)
Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is
tripled and the mass is doubled, then what is the new acceleration of the sled?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
9)
Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is
tripled and the mass is halved, then what is the new acceleration of the sled?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
10) A 5-kg object is sliding to the right and encountering a friction force which
slows it down. The coefficient of friction ("mu") between the object and the
surface is 0.1. The applied force is 50 N. Determine
the force of gravity, the normal force, the force of
friction, the net force, and the acceleration. (Neglect
air resistance.)
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