Download 4.1 The Concepts of Force and Mass

Chapter 4
Forces and Newton’s
Laws of Motion
Chapter 4: Forces and Newton’s Laws
•Force, mass and Newton’s three laws of motion
•Newton’s law of gravity
•Normal, friction and tension forces
•Apparent weight, free fall
•Equilibrium
Force and Mass
Forces have a magnitude and direction – forces are vectors
Types of forces :
• Contact – example, a bat hitting a ball
• Non-contact or “action at a distance” – e.g. gravitational force
Mass (two types):
• Inertial mass – what is the acceleration when a force is applied?
• Gravitational mass – what gravitational force acts on the mass?
Inertial and gravitational masses are equal.
Arrows are used to represent forces. The length of the arrow
is proportional to the magnitude of the force.
15 N
5N
Inertia is the natural tendency of an object to remain at rest or
in motion at a constant speed along a straight line.
The mass of an object is a quantitative measure of inertia.
SI Unit of Mass: kilogram (kg)
SI unit of force:
m
1N  kg   2
s
Newton (N)
 kg  m

2
s

Newton’s Laws of Motion
1. Velocity is constant if a zero net force acts


a  0 if F  0
2. Acceleration is proportional to the net force and inversely
proportional to mass:

a

F
m


so F  ma
Force and acceleration are in the same direction
3. Action and reaction forces are equal in magnitude and
opposite in direction
Newton’s First Law (law of inertia)


Accelerati on a  0 if F  0
Object of mass m

Velocity v  constant
The velocity is constant if a zero net force acts on the mass.
That is, if a number of forces act on the mass and their vector sum is
zero:

 
Fnet  F1  F2  ....  0
So the acceleration is zero and the mass remains at rest or has
constant velocity.
Individual Forces
4N
10 N
Net Force
6N
5N
3N
37 
4N
Some Examples:
Why does a falling object reach so called terminal velocity?
The force due to gravity is acting down,
accelerating the object toward the ground.
The object also experiences the force due
to friction with molecules in the air, which
is a result of a complicated interplay between
air pressure, wind speed and direction, and
the shape as well as the speed of the object.
If the object falls long enough, at some speed
the frictional force will be equal and opposite to the force due
to gravity. The forces exactly cancel producing a zero net
force:
And the velocity is constant: i.e. Terminal velocity!
Why do you have to keep your foot on the accelerator pedal, even if you
want to go at a constant velocity?
The weight of the car produces friction between the tires and
the road and the car will slow down due to this friction unless you
continue to accelerate.
Newton’s First Law
It was a revolutionary idea that objects continue to move if no
force acts:
– experience shows that a force is needed to keep objects
moving (friction)
– it was believed that some cosmic force keeps the planets
moving in their orbits
In the absence of friction, objects continue to move at constant
velocity if net force is otherwise zero (Nothing is done to the
object).
If the net force, including the force due to friction, is zero,
objects move at constant velocity (Something is pushing or pulling
to offset the force due to friction).
Newton’s First Law

FN
m
A crate is at rest on the ground:


v  0 and a  0
What forces act on the crate?

w
the weight:


w  mg
According to Newton’s first law, there must
be another force so the net force acting on
the crate is zero.
It is the normal force of the ground acting on the crate
 
FN  w  0


FN  w

FN
so the crate remains at rest
Inertial Reference Frame
Can be defined anywhere:
• right here
It is a coordinate system, (x, y, z)
y
• in your car...
x
An inertial reference frame is one that is not accelerated (moves at
constant velocity, including zero velocity).
• the law of inertia (first law) applies in an inertial frame – objects at
rest remain at rest if no net force acts on them.
• law of inertia does not apply in an accelerated (non-inertial) frame.
Example:
Driving around a corner – velocity changes, force has to be
applied to keep objects from moving – a non-inertial frame.
Newton’s Second Law
Says what happens if the net force acting on a mass is not zero.
The mass accelerates:
Acceleration,
 
a  Fnet

Fnet =
net force acting on the mass
proportional to
Introduce the mass:

a

Fnet
m


or Fnet  ma
m is the “inertial mass”, a measure of how difficult it is to accelerate
an object.
Newton’s Second Law
m = 1850 kg
A free-body
diagram shows only
the forces acting on
the car
Two people push a car against an opposing force of 560 N.
One exerts 275 N, the other 395 N of force on the car.
What is the net force acting on the car?
What is the car’s acceleration?
Problem:
A catapult on an aircraft carrier accelerates a 13,300
kg plane from 0 to 56 m/s in 80 m. Find the net force
acting on the plane.
Fnet  ma
(acceleration along a straight line)
What is a?
v 2  v 02  2ax
or
562  0  2a  80
so a  562 / 160  19 .6 m/s 2
Therefore
Fnet  (13,300 kg )  (19.6 m/s 2 )  261,000 N
The direction of force and acceleration vectors can be taken
into account by using x and y components.


 F  ma
can be decomposed into
Fx  ma x
Fy  ma y
Then solve the equations separately in each direction.
Problem 4.11
What is the acceleration of the block in the horizontal
direction?
Work out the components of
forces in the x-direction.
x
59 N
No friction
33 N
Problem 4.88
A 75 kg water skier is pulled by a horizontal force
of 520 N and has an acceleration of 2.4 m/s2.
Assuming the resistive force from water and wind is
constant, what force would be needed to pull the
skier at constant velocity?
Problem 4.4
A special gun is used to launch objects into orbit
around the earth. It accelerates a 5 kg projectile to
4x103 m/s by applying a force of 4.9x105 N.
How much time is needed to accelerate the projectile?
Problem 4.14:
A 41 kg box is thrown at 220 m/s against a barrier. It is
brought to a halt in 6.5 ms.
What is the average net force that acts on the box?
m = 1300 kg
Wind
Paddling
Paddling: force FP of 17 N, to east
Wind: force FW of 15 N, 67o north of east
Find ax, ay for the raft.
The net force is:
Problem 4.17:
A 325 kg boat is sailing 15.0 degrees north of east at
2.00 m/s. 30 s later, it is sailing 35.0 degrees north of
east at 4.00 m/s. During this time, three forces act on the
boat:

Auxiliary engine : F1 31.0 N to 15.0 degrees north of east

Water resistance: F2 23.0 N to 15.0 degrees south of west

Wind resistance : Fw

Find the magnitude and direction of the force Fw .
Give the direction with respect to due east.
Apply Newton’s Second Law:
  

F1  F2  Fw  ma
First, find the average acceleration :
north

vi  2 m/s
  15

vf  4 m/s
  35
east
t  30 sec

vf

vi
  
v  vf  vi
Then use Newton’s second law:
north

m a  24.1 N
 15
F2  23 N

Fw  ? 
F1  31 N
 ?
east
 
F1  F2  8N