UNIT 1 - ENERGY & MOTION
Lesson 1.3 FORCES
Overview
This lesson deals with the effects of forces on motion.
On completion of the lesson, you should be able to
discuss Newton’s First and Second laws. You should
be able to describe the effects of forces such as
friction and centripetal force. You should also be able
to estimate the net force when two or more forces are
acting in the same or opposite directions and the
resultant force when two forces are acting at right
angles to each other.
ToDo
Watch the video presentation.
Carry out the activities.
Read through the lesson notes and do the exercises.
Refer to the solutions and check your answers.
At
home: Prepare for
Lab 1.3 by reading the instructions and collecting the necessary
materials and equipment.
Similarly, prepare for the two activities
in Lesson 1.4 and
test the equipment.
ACTIVITIES
Electrostatic Forces:
Use a sheet of plastic (acetate) and some foam peanuts to
show how charged articles are attracted or repelled by
each other.
Magnetic Forces &
Motors: Use a pair of permanent magnets to show how
magnets attract and repel each other.
Open up one or two small electric motors and identify the
magnets and/or electromagnets inside the motors. Show how
magnetic forces cause electric motors to rotate.
Activity
1.3.1: Electrostatic Forces
Purpose: To
demonstrate the forces of attraction and repulsion
between electrically charged objects
Equipment:
Plastic sheet (overhead
transparency or piece of clear pvc)
Foam peanuts or foam chips
Clean woolen cloth
Procedure:
Note: This
experiment will probably not work if the humidity is high.
- Rub the transparency
with the woolen cloth and hold it near to the
foam peanuts.
- The peanuts should be
attracted by the transparency and stick to it.
- Touching the peanuts
or the sheet with a metal conductor may remove
the electrical charge
Activity 1.3.2: Magnets
Purpose: To
demonstrate forces of attraction and forces of repulsion
between different magnetic poles.
Materials and Equipment:
2 or 3 magnets
Procedure:
- Hold like poles of
magnets close together and observe their tendency
to repel each other.
- Hold unlike poles
close together and observe the tendency of the
magnets to atract each other.
- Observe the effect of
distance on the strength of the attractive and
repulsive forces
Activity
1.3.3: Electric Motors
Purpose: To
demonstrate forces that drive electric motors.
IMPORTANT
SAFETY NOTE
Do not to use sources of electrical current that are
capable of producing voltages in excess of 30 volts when
testing or demonstrating the operation of electric motors.
Procedure
- Open up a battery
powered or low voltage electric motor and
identify the coils in the rotor.
- Show how the
commutator changes the polarity of the
electromagnets in the rotor.
- If possible, connect
the segments of the commutator for one coil to a
voltage source and show how this causes the rotor
to turn in a particular direction.
- Reverse the polarity
of the connection to the coil and show how the
rotor moves in the opposite direction.
Velocity
Velocity is speed in a particular direction.
Acceleration
Acceleration is a change in velocity over a particular
period of time.
Average Speed and
Velocity
Average speed is the ratio of the change in distance
along a path to the time interval over which the change
takes place.
Average velocity is the ratio of the change in position
to the time interval over which the change takes place.
Friction
Friction opposes movement and creates internal energy.
Friction is the force that opposes the motion of two
objects or materials in contact with each other.
Tension forces
Forces applied at the ends of an object that tend to
increase its length. The forces are equal and opposite
and tend to be resisted by intermolecular forces.
Compression forces
Equal and opposite forces that tend to decrease the
length of an object.
Centripetal force
The force that causes a change in direction of a moving
object. If an object is moving in a circular path, it
will accelerate continually towards the center of the
circle.
Velocity
Velocity is speed in a particular direction. If something
changes direction while it is moving at a constant speed,
it's velocity will change. Quantities that need to be
measured in a particular direction are called vectors.
Velocity is a vector quantity. Speed does not depend on
direction and is not a vector quantity.
Average and
Instantaneous Speeds and Velocities
When speeds and velocities are measured, the period used
in determining the speed or velocity needs to be taken
into account.
Speed is the ratio of the
change in distance along a path to the time interval over
which the change takes place. This is the average speed
over the particular time interval.
Velocity is the ratio of
the change in position to the time interval over which
the change takes place. This is the average velocity over
the particular time interval.
Instantaneous values for
speed or velocity are more difficult to determine because
they occur in extremely short periods. (strictly:
infinitely small periods) If we are able to plot changes
in speed or velocity, we can use the graph to estimate
speeds or velocities at a particular instant.
Acceleration
Acceleration is a change in velocity over a particular
period of time.
Acceleration occurs when
speed varies and/or direction varies. Acceleration can be
positive or negative. It is a vector quantity and the
value (positive or negative) depends on the direction in
which the acceleration occurs. Deceleration may be
regarded as negative acceleration but the actual value (positive
or negative) depends on the direction in which the
acceleration is taking place.
Force:
Typically a push or a pull. A force influences the motion
or shape of an object. When a force affects the motion of
an object it accelerates the object by increasing or
decreasing its velocity.
A force can cause
acceleration. According to Newton’s first and second
laws, an object won’t accelerate unless a force acts
on it. The amount of acceleration is proportional to the
size of the force and is inversely proportional to the
mass of the object.
Vector quantity
A vector quantity is a quantity that has both magnitude
and direction. A quantity that does not have a specific
direction is known as a scalar quantity. Velocity,
acceleration and force are vector quantities. They act or
occur in a particular direction.
Resultant
The combined effect of two or more vectors. The resultant
is a single vector with its own direction that represents
the net result of the vectors acting or occurring
together.
Force field
A region in which a force has an effect. For example, the
strengths of magnetic and gravitational forces vary with
distance from the object or objects responsible for the
forces. The force field exists within the range in
distance over which theforce has effect.
Gravitational force
The attraction between any two objects as a result of
their mass. The acceleration caused by gravity at the
earth’s surface = 9.81 m/s2
The gravitational force on
an object in a vertical direction towards the earth at
the earth’s surface is equivalent to 9.81 N/kg.
Friction
Friction opposes movement and creates internal energy.
Friction is the force that opposes the motion of two
objects or materials in contact with each other.
Friction acts in the
opposite direction to the relative motion of the two
objects or materials. Friction can occur when solids,
liquids and gases are in contact. Friction generally
results in an increase in internal energy of the
materials in contact.
There are two types of
friction: static friction and dynamic friction. Static
friction is usually slightly larger than dynamic friction
and opposes the initial movement of one material relative
to the other. Once movement starts, dynamic friction
occurs as long as there is relative movement.
Electric force
The force between electrically charged particles. Like
charges repel each other.
Unlike charges attract
each other.
Magnetic force
Typically the force between two or more permanent magnets
and/or electromagnets. Magnets have poles and like poles
repel each other whereas unlike poles attract each other.
Magnetic force also refers to the force between two
moving charges. Electrons move in conductors carrying
electrical current. If two conductors or wires are close
together and conduct electricity in the same direction,
the conductors will repel each other. If the conductors
carry current in opposite directions, they will attract
each other.
Intermolecular forces
The attractive or repulsive forces between molecules or
particles (atoms, ions) that make up a material. The
strength and direction of the forces vary with distances
between particles.
Tension forces
Forces applied at the ends of an object that tend to
increase its length. The forces are equal and opposite
and tend to be resisted by intermolecular forces.
Compression forces
Equal and opposite forces that tend to decrease the
length of an object.
Centripetal force
The force that causes a change in direction of a moving
object. If an object is moving in a circular path, it
will accelerate continually towards the center of the
circle. This acceleration is caused by a force of
attraction known as a centripetal force.
Centrifugal force
Strictly speaking, centrifugal force is not a force
because it does not cause acceleration in its direction.
Centrifugal force is the
name associated with the force that is equal and opposite
to centripetal force.
For example, the tension
in a rope that is used to swing an object in a circular
path is a result of the force needed to accelerate the
object towards the center of the circular path. The
tendency for the object to move away from the center of
the circle is its natural tendency to continue its motion
in a straight line.
Example
1.3.1: Calculation of work
How much work is done if an object is pushed 1 meter
along the surface of a table and the frictional
resistance is 2 Newtons?
Solution
The work done in moving it across one meter of the table’s
surface is 2 Newton-meters or 2 Joules.
Example
1.3.2 Net Force
A skydiver with a mass of 80 kg has a gravitational force
of 9.81 N/kg acting on her as she falls. If the drag due
to air resistance is equivalent to 300 N, what is the net
force on the skydiver? In what direction is it acting?
Solution
The gravitational force on the skydiver is = 80 x 9.81 =
784.8 N
The net force is thus 784.8
– 300 = 484.8 N acting downwards.
Example
1.3.3 Resultant Force
A hovercraft has two fans that enable it to move about.
One fan creates pressure between the hovercraft and the
ground that results in a lifting force of 5000 N. A
second fan, mounted horizontally, creates a horizontal
thrust of 2000 N. What is the resultant of these two
forces acting on the hovercraft.
Solution
The two forces act at
right angles to each other.
The net effect of the two forces - the resultant - can be
found by drawing lines that represent the forces and
combining them geometrically. The lines are drawn in the
relative directions of the forces and the lengths of the
lines are in proportion to the sizes of the forces.
The forces and the
resultant are shown on the diagram below. (This is called
a vector diagram)
One method of finding the
resultant of two vectors that are at right angles to each
other is to draw the two forces and draw two similar
lines to make a rectangle. The resultant is found by
measuring the distance and angle of the line from the
intersection of the forces to the opposite corner of the
rectangle.
The resultant of the two
vectors in this example can be found by completing the
rectangle as follows:
We can use trigonometry to
calculate the relative direction of the resultant:
The tangent of the angle,
a , between the resultant and the horizontal = 5000 /
2000
Tan a = 2.5.
a is therefore = tan-1
2.5. This is = 68.2º from the horizontal.
We can also use
trigonometry to calculate the size of the resultant:
Sin 68.2º = 5000 /
Resultant
Resultant thus = 5000 /
sin 68.2º = 5385.1 N acting at an angle of 68.2º (from
the horizontal)
A simpler way to calculate
the size of the resultant is to use Pythagoras' theorem
and say that (Resultant)2 = 50002 +
20002
Review
Questions
- A racing car takes
180 seconds to circle a track with a distance of
6000 meters. What is it's average velocity during
this time?
- If the racing car
travels at a constant speed of 33.33 meters per
second around the track, does it accelerate?
- What effect can a
force have on an object?
- The Newton is the SI
unit of force. How is it defined?
- List five common
types of force
- Can electrostatic
forces be attractive and repulsive? Why?
- If an object travels
at 3 meters per second in a straight line, is it
accelerating?
- If an object travels
at 3 meters per second in a circular path, is it
accelerating?
- If a water bomb
weighing 200 grams (0.2 kg) is dropped from a
height of 10 meters above ground, what will its
velocity be on impact? (Ignore the effect of air
resistance)
- What is the force
that acts to oppose the motion of two surfaces,
objects or materials in contact with each other?
- The water pressure in
a pipe at the outlet of a pump is 300,000 Pascals
or Newtons per square meter). How much force does
the water exert on 0.005 square meters of the
inside surface of the pipe?
- If an object has a
force of 3 N. acting on it and a force of 2 N
acting on it in the opposite direction, what is
the net (or resultant) force acting on it?
- An object on a flat
surface has 2 forces acting on it. The forces are
parallel to the surface but in different
directions as shown in the diagram below. What is
the resultant force on the object?
HOMEWORK
Select one or more of the recommended
activities for Lesson 1.4, collect the items needed and test the
procedure before demonstrating the activity during the
next theory lesson.
W = Fd Work = force x distance
Where: W = work (J)
F = force (N)
d = distance (m)
F = ma Force = mass x acceleration
Where: F = force (N)
m = mass (kg)
a = acceleration
P = F / A Pressure = force per unit area
Where: P = pressure
(N/m2 or Pa.)
F = force (N)
A = acceleration (m/s2)
Epress = PV Pressure energy = pressure x volume
Where: Epress
= pressure energy of a certain volume of
fluid (J)
P = pressure of fluid (Pa or N/m2)
V = volume of fluid (m3)
Espring
= ½ k D l 2 Energy stored in spring
= ½ x spring constant x (increase
in length of spring)2
Where: Espring
= energy stored in spring (J)
k = spring constant (N/m)
and D l = change in length of
spring (m)
Velocity:
Speed in a particular direction.
Acceleration: The rate of change in velocity.
Acceleration is a change in velocity over a particular
period of time.
Force: Typically a push or a pull. A force influences
the
motion or shape of an object.
Newton’s First Law: If an object is at rest or
if its speed and direction are constant, then the
resultant force on it is zero. If there is no net force
on an object, there is no acceleration.
Newton’s Second Law: Simply: Force = mass x
acceleration. The acceleration of a body is directly
proportional to the net force on it and inversely
proportional to its mass. F = ma
Vector quantity: A vector quantity is a quantity that
has both magnitude and direction
Resultant: The combined effect of two or more vectors.
Resultant force: The combined effect of two or more
forces.
Newton: The SI unit of force. 1 Newton (N) is the
force needed to accelerate 1 kilogram by 1 meter per
second per second. 1 N = 1 kg.m/s2
Force field: A region in which a force has an effect.
Gravitational force: The attraction between any two
objects as a result of their mass.
Friction: Friction is the force that opposes the
motion of two objects or materials in contact with each
other.
Electric forces: The attractive or repulsive forces
between electrically charged particles.
Magnetic forces: Typically the force between two or
more permanent magnets and/or electromagnets. Magnetic
forces also refer to the forces between two moving
charges.
Intermolecular forces: The attractive or repulsive
forces between molecules or particles (atoms, ions) that
make up a material.
Tension forces: Forces applied at the ends of an
object that tend to increase its length. The forces are
equal and opposite and tend to be resisted by
intermolecular forces.
Compression forces: Equal and opposite forces that
tend to decrease the length of an object.
Centripetal force: The force that causes a change in
direction of a moving object.
Centrifugal force: Centrifugal force (not a true
force) is the name associated with the force that is
equal and opposite to centripetal force.
Lesson 1.3 Force
- The average velocity
of the car is zero because it's net displacement
after completing the distance around the track is
zero.
- Yes. The direction of
the motion around the track changes. An object
accelerates when it's speed changes and/or it's
direction of movement changes.
- A force influences
the motion or shape of an object. When it
influences the motion of an object, a force
causes acceleration. It can also cause
deformation of the object
- The Newton is the SI
unit of force. 1 Newton (N) is the force needed
to accelerate 1 kilogram by 1 meter per second
per second. 1 N = 1 kg.m/s2
- Five common types of
force: Tension, compression, gravitation,
magnetic attraction or repulsion & friction.
There are many other types of forces such as
electrostatic attraction or repulsion,
intermolecular forces, etc.
- Yes. Like charges
repel each other. Unlike charges attract each
other.
- No.
- Yes. According to
Newton’s law, a body will remain at rest or
continue its motion in a straight line unless an
external force acts on it. Whenever the motion of
an object is affected by a force, it accelerates.
When an object moves in a circular path, it is
accelerating in the direction of the applied
force which is towards the center of the circular
path.
- As the water bomb
falls, it’s gravitational potential energy
is converted to kinetic energy. When it reaches
the floor, all of its gravitational potential
energy will have been converted to kinetic energy.
The gravitational potential energy at 10 m above
the floor = mgh = 0.2 kg x 9.81 J/kg.m x 10 m =
19.62 J.
When it reaches the floor ½mv2 = 19.62
J.
v2 = 19.62 /( ½m) = 19.62 / (0.5 x 0.2)
= 196.2 m2/s2
v = v(196.2) = 14 m/s
- Friction.
- 1 Pascal = 1 Newton
per square meter.
300,000 Pa exerts a force equivalent to 300,000 N
on 1 m2.
300,000 Pa. exerts 0.005 x 300,000 N on 0.005 m2
= 1,500 N on 0.005 m2.
- 1 N in the same
direction as the 3 N force.
- An object on a flat
surface has 2 forces acting on it. The forces are
parallel to the surface but in different
directions as shown in the diagram below.
Using Pythagoras' Theorem,
(302 + 402 = 502
)
The resultant force on the object is thus = 50 N
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