Download The Nature of Force

The Nature of Force
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Bulldozers exert huge forces to move soil and rocks from one place to another. Children
apply small forces to form modeling clay into interesting shapes. Force is defined as a
or
on an object. A force applied to an object has a tendency to change
the shape and/or motion of the object.
Force is a vector quantity. Each force has a certain strength or magnitude. Each force also
has a certain direction. The size of a force can be described using an adjective like large,
small, huge, and insignificant. Scientists describe the size of a force with a numeral and a
unit. For example: 10 N. Adjectives such as [forward], [backward], [up], and [down] state
directions. Compass directions such as north [N], south [S], and [N 30° E] are also
accepted ways of describing the direction of a force.
Measuring Force
The symbol for force is F. The SI unit of force is the newton (N) named in honour of Sir
Isaac Newton the famous English physicist. One newton is roughly equal to the force of
gravity of the Earth on a medium sized apple. (In other words, the force needed to lift an
apple.) In base units, a newton is equal to a kilogram metre per second squared (1 N = 1
kg.m/S2).
Force is generally measured using a
. A force applied to an elastic
spring, causes it to stretch. As the spring stretches, the elastic force exerted by the spring
increases. When the applied force is balanced by the elastic force, the spring stops
stretching and the applied force is read from the calibrated scale.
Free-body Diagrams
We know that a vector quantity is represented on a diagram by a directed
line segment called a vector. The length of the line segment represents the magnitude,
and the arrowhead shows the direction. A scale and reference co-ordinates are included in
the diagram. A single force seldom acts on an object. It is often helpful for physicists and
engineers to draw a vector diagram showing all the forces acting simultaneously on an
object. This helps them to picture and analyze the situation. Such a diagram is called a
free-body diagram because the object is shown isolated from its surroundings.
To draw a free-body diagram:
 Draw a diagram of the object isolated from its surroundings.
 Locate with a point, the approximate centre of mass of the object.
 From the point draw a force vector to represent each force acting on the object.
 Do not include forces that the object exerts on other objects.
The free-body diagram for the mass suspended from a spring would look like this:
Notice that two equal forces (the force of gravity and the elastic force) act in opposite
directions on the mass. The spring scale is not shown because we are drawing a free-body
diagram of the mass, not the spring scale.
Two other forces commonly act on an object.
1. The normal force is the force that acts on an object perpendicular to the surface
on which it is resting.
2. The force of friction acts in the opposite direction to the way the object is
moving or is tending to move.
Sample Problem 1
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Draw a free-body diagram to show the following forces acting on a coasting car:
a force of gravity F G of 15000 N [down]
a normal force exerted directly up by the road F n of 15000 N
a force of friction Ff of 3500 N [back).
Solution A free-body diagram shows all the forces that are acting on an object, is drawn
to scale, and helps us to analyze the situation.
Finding the Sum of Forces
It is often necessary to find the sum of several forces acting on an object. The total force
is called the
. The net force is that single force that has the same
effect as several forces acting simultaneously. We can determine the net force by finding
the vector sum of all the forces acting on the object. Other names for the net force are the
and the
.
Adding Collinear Forces As with other vector quantities, forces that are along the same
straight line (collinear) are added by finding their sum in the direction chosen as positive.
Sample Problem 2
A tow truck starting to tow a damaged car exerts a force F of 4500 N [E] on the car.
A 1500 N [W] force of friction F f slows down the car's motion.
The force of gravity on the car F G is 8400 N [down].
a) Draw a free-body diagram for the car. b) Calculate the net force on the car.
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Adding Non-Collinear Forces Sometimes forces are non-collinear. This means they do
not always act along the same straight line. For example, a football player may be tackled
by several opposing players at the same time. How can we find the net force on the
player? Fortunately, both collinear and non-collinear forces can be added using the tail to
tip method.
Sample Problem 3
Two football players tackle a rival fullback, exerting two horizontal forces on him at the
same time. The forces are 350 N [N] and 250 N [W]. What is the net force on the
fullback?
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Name:
Questions:
1. Draw a separate vector diagram for each of the following forces:
a) 4 N [W]
b) 1500 N [S30° E]
c) 850 N [S]
d) 25 N [E]
2. The total force of gravity on Kendre and her motorbike is 1820 N [down]. The
engine exerts a force of 650 N [forward]. The air resistance acting on Kendre and
the bike is 230 N [backward]. The friction between the tires and the road is 110 N
[backward]. The normal force exerted by the road is 1820 N [up].
a) Draw a free-body diagram for the system that includes Kendre and her
motorbike.
b) Calculate the net force on Kedre and the motorbike.
3. Amanda is pulling a heavy wagon along the sidewalk by exerting a force of 12
N [E] on it. A force of friction of 10 N opposes the motion. The force of gravity on
the wagon is 20 N.
a) Draw a free-body diagram showing all the forces acting on the wagon.
b) Determine the net force on the wagon.
4. Three horizontal forces act on a basketball: 40 N [S]; 30 N [E]; 20 N
[N 45° E]. Draw a tail to tip vector diagram and calculate the net horizontal force
on the basketball.
5. Tom, Claude, and Elena are tugging on a rubber tube in shallow water. Tom
exerts a force of 40 N [N 30° E], Claude a force of 30 N [W], and Elena a force of
50 N [S 45° W].
a) Draw a force diagram showing the three horizontal forces acting on the tube.
Ignore the vertical forces.
b) What is the net horizontal force acting on the tube?