• Force: a push or a pull exerted on an object.
• Mechanical forces
require the objects to be in physical contact.
The study of force is often called DYNAMICS.
• Friction is an example of a mechanical force.
• Sliding friction always acts in the opposite
direction as the motion of the object.
• Non-mechanical forces can act at a distance.
• e.g. gravity, electric force, magnetic force.
Force is a vector quantity
Gravitational Force
Electric Force Magnetic
Force
Force was first mathematically defined by Sir Isaac Newton (1642-1727)
NEWTON’S FIRST LAW
• An object will remain at constant
velocity until an unbalanced force acts upon it.
Free-body diagrams are used to illustrate the forces acting on an object.
e.g. a 20 000-N stationary rock
Free-body diagram FN
Fg Fg= force of gravity
FN= normal force or “support force”
Fnet = Fg + FN = (-20 000 N) + (+20 000 N) = 0 N
Balanced Forces
No
acceleration
e.g. A 0.50 N air-hockey puck on a frictionless surface, moving with a constant speed of 15 m/s.
FN
Fg
Fnet = Fg + FN = (-0.50) + (+0.50) = 0 N
Balanced Forces
No
acceleration
e.g. a girl bikes along at a constant speed of 5.0 m/s.
FN
Fg
FA Ff
Fnet = Ff + FA = 0 N x-direction
Fnet = FN + Fg = 0 N y-direction
Balanced Forces
No
acceleration
e.g. an accelerating race-car
FN
Fg
FA Ff
Unbalanced Forces
Acceleration
e.g. a falling car
Ff
Fg
Unbalanced Forces
Acceleration
e.g. a falling car with open parachute:
Ff
Fg
Balanced Forces
No
acceleration
a m 1
a F net
a m F net
NEWTON’S SECOND LAW
• An unbalanced force acting on an object
causes it to accelerate uniformly.
• The acceleration is proportional to the force
• The acceleration is inversely proportional to the mass (called the LAW OF
INERTIA)
Let’s test the Newton’s Second Law Fnet = ma, by
analyzing the relationship between force and acceleration
Conclusions:
a
Fnet
• Fnet and a are directly proportional
• According to Fnet = ma, the slope should be equal to (mass)-1
net net
net
m F a
m a F
ma F
1
Slope
What would the graph for a more massive object look like?
More massive objects require more force to accelerate. This property of mass is called INERTIA.
Less massive
More massive
To verify this compare the measured mass to the reciprocal of the slope.
e.g. a golf ball has little mass and therefore little inertia;
a truck has much mass and therefore much inertia
NEWTON’S LAW & GRAVITY
• The force of gravity acting on an object is often called weight
Force of gravity or
WEIGHT (N) Mass (kg) Acceleration due to gravity (m/s2)
e.g. Calculate the weight of a 3.0-kg human head on the surface of Planet Earth.
29 N
Fg =mg explains why all objects fall at the same rate of acceleration if air resistance is negligible.
… when air resistance is a factor objects fall with varying rates of acceleration.
Terminal velocity and sky-diving:
NEWTON’S THIRD LAW
• If OBJECT A exerts a force on OBJECT B, then OBJECT B will exert a force on OBJECT A of equal magnitude and opposite direction.
Girl exerts force on wall
Wall exerts force on girl
Air exerts force on balloon Balloon exerts
force on air
Rocket exerts force
on fuel exhaust
Fuel exhaust exerts force
on rocket
Ball exerts force on cannon
Cannon exerts force on ball
Gun exerts force on bullet
Bullet exerts force on gun
Boy runs and jumps from canoe to dock:
Boy exerts force on canoe
Canoe exerts force on boy
Skater exerts a force on ice
Ice exerts a force on skater
• Friction is an example of a mechanical force.
• Friction always acts in a direction opposite to the motion of the object.
•Friction can be measured by
seeing how much force is needed to slide an object
along at a constant speed
FA Ff
Ff = Fa
• The force of friction
depends on two variables
Normal force – force perpendicular to the surface (i.e. the
support force FN or Fs)
Coefficient of friction between the two
surfaces (μ or “mu”)
Fg
N g
F F FN
… pronounced “mew”
N
f F
F
Force of friction
(N)
Coefficient of friction
(NO UNITS)
Normal force (N)
For objects on flat surfaces:
mg F
F F F
f
g N f
FN
Fg
…for flat surfaces
Example:
1. A rocked is accelerating upward at 20 m/s2 a) How much force would the
thrusters of a 500-kg rocket have to apply to the rocket in order to achieve this?
(Assume no air resistance)
b) How much force would an astronaut’s seat have to apply to her as she
accelerated upward with the rocket?
(mastronaut = 65 kg) Fa
Fg Fa (applied by seat)
Fg
Does that astronaut feel heavier, lighter or normal as the rocket accelerates upward?
HEAVIER!
Fg FN
• A stopped astronaut: • An astronaut accelerating upward
The force felt by the astronaut
Fg FN
This force would register
on a weight scale!
This force would register
on a weight scale!
e.g. Scale reading = 500 N e.g. Scale reading = 900 N
F
netHow would the astronaut feel if the rocket was traveling upward at a constant velocity?
F
net=0
Fg FN
Fg FN NORMAL
e.g. Scale reading = 500 N e.g. Scale reading = 500 N
How does he feel traveling upward with a downward acceleration?
LIGHTER!
Fg FN
Fg FN
e.g. Scale reading = 500 N e.g. Scale reading = 100 N Fnet
SUMMARY v-t graph: A trip up and then back down again:
v
+
-
Going up,(+) accel Going up,(0) accel Going up,(-) accel Going down,(-) accel Going down,(0) accel Going down,(+) accel
“Heavy” “Normal” “Light” “Light” “Normal” “Heavy”
t
“Normal”
Stopped,(0) accel
… now let’s add a d-t graph:
v
+
-
t
t
d
How does he feel if the downward acceleration is equal to 9.81 m/s2?
Vomit Comet Movie
WEIGHTLESS!
The same effects happen in elevators…
…as you will observe in the lab.
Example Problems (Vertical Forces)
1) An astronaut with a mass of 75.0 kg is astonished to find that she weighs 500 N during a trip in her rocket.
Calculate the rocket’s vertical acceleration.
3.14 m/s2 down
2) Jimmy (mass = 65 kg) is hanging from a newton-metre while riding an elevator. If the elevator is accelerating at 7.0 m/s2, upward, then what would be the reading on the newton- metre?
