Foundation course - PHYSICS
Lecture 5-2: Force and motion
Dynamics of solid bodies
● Acceleration and force
● Newton’s laws of motion
● Some particular forces (normal, weight, tension, friction)
Naďa Špačková spackova@physics.muni.cz
Dynamics
Force
● is an interaction between objects
● is a vector (determined by its magnitude and its direction)
● magnitude is measured in units called newtons (N): 1 N = kg.m.s-2
Essential questions:
● Why objects move
● What can cause an object to accelerate
● What acts on an object and changes its velocity
It is a FORCE
Free-body diagrams:
● a physical representation
of forces acting on the
system
Dynamics of solid bodies
Acceleration is the result of an unbalanced force
acting on an object.
Ftable on book
Fhand on book
FEarth’s mass on book
Contact and field forces
Contact force:
● an object from the external
world touches the system and
exerts a force on it
Field force:
● the force affects the system
without touching
● examples: gravitational force,
electromagnetic force
gravitational force
electrostatic force
magnetic force
Combining forces
F2
= 100 N F1
= 100 N
Fnet
= 0 N
F2
= 100 N
F1
= 100 N
Fnet
= 200 N Fnet
= 100 N
F2
= 200 N F1
= 100 N
Net force: the vector sum of all forces acting on the object
Equal forces
Opposite directions
Equal forces
Same direction
Unequal forces
Opposite directions
Newton’s first law
Fnet=0 ⇒ a=0 a=0 ⇒ v=constant
If the net force is zero, then acceleration equals zero.
If acceleration is zero, then velocity does not change – it
means, the object is at rest or is moving with a constant
velocity.
Newton’s first law:
An object that is at rest will remain at rest, and an object that is moving will
continue to move in a straight line with constant speed, if the net force acting
on that object is zero.
Newton’s first law
Law of inertia
Inertia = the tendency of an object to resist changes in velocity
If the net force is zero, then an object is in equilibrium.
An object is in equilibrium if it is moving at a constant velocity (v = 0 is
a special case of the constant velocity).
Checkpoint question:
Which of the six arrangements correctly show the vector addition of forces F1
and
F2
to yield the third vector, which is meant to represent their net force Fnet
?
(a) (b) (c)
(d) (e) (f)
F1
F1
F1
F1
F1
F1
F2
F2
F2
F2
F2
F2
Equilibrium
● the object is in equilibrium, when the net force on an object is zero
● the object in equilibrium moves with constant velocity (or is staying at
rest)
Two forces acting
on the object
The equilibrant force has
the same magnitude and
opposite direction as the
resultant force
The resultant force
is a sum of
individual forces
To put the object in equilibrium, we must add the
equilibrant force.
FA
FB
FA
FR
FE
FA
+ FB
= FR
FE
= -FR
Acceleration and force
Velocity increases linearly
in time → acceleration is
constant
Applied force:
Fgreen
< Fred
< Fblue
The relationship between
force and acceleration is
linear → application of
equation for a straight line:
y = kx + b
Acceleration and force
When the mass increases, a greater force is needed to produce the
same acceleration.
The slope is reciprocal of the mass.
Using the equation for a straight line y = kx we obtain a =
Fnet
m
Newton’s second law
Newton’s second law:
the acceleration of an object is proportional to the net force and inversely
proportional to the mass of the object being accelerated.
a =
Fnet
m
⇒ Fnet= m⋅a
Forces are measured in newtons (N):
1 N = 1 kg.m.s-2
Force is a vector (size, direction)
If more than one force is acting on an object, it is necessary to determine the net
force (as a sum of individual forces).
Fnet
Fnet
F1
F1F2
F2
There are two horizontal forces acting on a block on a frictionless floor. If a third
horizontal force F3
also acts on the block, what are the magnitude and direction of F3
when the block is
(a) stationary
(b) moving to the left with a constant speed of 5 m/s?
3 N 5 N
Example: forces
Figure show three situations in which one or two forces act on a puck that moves over
frictionless ice along an x axis, in one-dimensional motion. The puck’s mass is m =
0.20 kg. Forces F1
and F2
are directed along the axis. In each situation, what is the
acceleration of the puck?
4 N 4 N2 N 1 N2 N
30°
Example: forces and acceleration
Weight
An object’s weight is the gravitational force (due to Earth’s mass)
experienced by that object:
The gravitational acceleration near Earth’s surface is 9.8 m.s-2
Weight is a force, the proper units are newtons (N).
Fg = m g = W
m … mass of the object
g … gravitational acceleration
The normal force
Fg
FN
● term normal means perpendicular direction of the force
● when a body presses against a surface, the surface deforms and pushes on
the body with as normal force FN
that is perpendicular to the surface
FN − Fg = may
FN = m g + m ay
FN = m(g + ay)
If objects are not accelerating, then ay
= 0
FN = m g
The normal force
FH
FH
Weight
Apparent weight
● acceleration of the system is upward, the net force must
be upward
● the upward force of the scale must be greater than the
downward force of your weight
● the scale reading is greater than your weight
Weightlessness – object’s apparent weight is zero
Example: force and acceleration
An elevator cab that weights 27.8 kN moves upward. What is the tension in the cable if
the cab’s speed is:
(a) increasing at a rate of 1.22 m/s2
(b) decreasing at a rate of 1.22 m/s2
?
The tension force
Body attached to a cord
● the cord pulls on the body with force T directed away from the
body and along the cord
● the cord is massless and unstretchable and it exists only as a
connection between two objects
● the cord pulls on both bodies with the same force magnitude T
Example: inclined planes
The mass of the block is 8.5 kg and the angle θ is 30°.
Find:
(a) the tension in the cord
(b) the normal force acting on the block
(c) If the cord is cut, find the magnitude of the resulting
acceleration of the block. (Assume no friction)
Newton’s third law
All forces occur in interaction pairs
Interaction pair
● a set of two forces that are in opposite
directions, have equal magnitudes, and
act on different objects
● sometimes called action-reaction pair
● both forces either exist together or not at
all
Newton’s third law:
When two bodies interact, the forces on the
bodies from each other are always equal in
magnitude and opposite in direction.
FA on B =−FB on A
Earth
table
ball
FBE
FEB
Earth
table
ball
FBT
FTB
The friction force
motion
Ft
The frictional force is parallel to the surface
and directed so as to oppose the sliding.
Friction is due to bonding between the body and
the surface.
body
surface
Friction
⃗Fs⃗F
⃗Fs⃗F
⃗Fd⃗F
⃗Fd⃗F
⃗a
⃗v
object at rest moving object
F(t)
Kinetic friction
● acts on moving objects
● is exerted on one surface by another when the two surfaces rub against
each other because one or both surfaces are moving
Static friction
● is the force exerted on one surface by another when there is no motion
between the two surfaces
Kinetic and static friction
Normal force [N]
Kineticfriction[N]
sandpaper
rough table
highly polished table
The slope of the line on a kinetic friction
force v. normal force graph is called the
coefficient of kinetic friction, μk
.
Ff ,kinetic=μk FN
Ff ,static≤μs FN
μs
is the coefficient of static friction
between the two surfaces
The friction forces Ft
are always
perpendicular to the normal force.
A girl, who has a mass of 45 kg, is going down
a slide sloped at 27°. The coefficient of kinetic
friction is 0.23. How fast does she slide 1.0 s
after starting from rest?
Example: inclined planes
Example: inclined planes
+y
+x
Fg
+y
+x
Fg
Fn
Ff
+y
+x
Fg
Fn
Ff Fnet