Applications of Newton’s Laws
Chapter 5
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The fundamental forces of
nature
• Gravitational interactions – dominant in
the macroscopic world
– Weight and free fall
– Planetary orbits
• Electromagnetic interactions – dominant in
the microscopic world
– Electric forces
• Static electricity
• Contact forces – normal, friction, etc.
– Magnetic interactions – caused by moving
electric charges
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Fundamental forces of nature
• Strong interaction
– Holds the nucleus of an atom together
– Also called nuclear force
• Weak interaction
– Responsible for beta decay –
radioactivity – by converting a neutron
into a proton, and electron, and a
neutrino.
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Current theories
• Electroweak interaction
• Grand unified theory – GUT
– Unites strong, electromagnetic, and weak
• Theory of everything – TOE
– Unites all four fundamental forces
• All speculative theories with many
unanswered questions.
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Friction
• When you slide a heavy box across the
floor
• You have to push with a strong enough
force to get it moving.
• Once it is moving, you can keep it moving
with less force than it took to get it started.
• If you make the box lighter, you need less
force than before to start it and to keep it
moving.
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Forces from a surface
• When an objects rests or slides on a
surface,
• The surface exerts a normal force
perpendicular to the surface
• And a frictional force parallel to the
surface.
• The direction of the frictional force is such
that it always opposes the relative motion
of the two surfaces.
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Kinetic Friction
• The frictional force that acts when a
body slides over a surface is called
kinetic friction.
• Its magnitude is given by:
f k  k FN
Magnitude of normal force
Coefficient of kinetic friction
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Static Friction
• The frictional force that acts on a body that is
resting on a surface is called static Friction.
• Static friction is what resists the beginning of
motion and makes it hard to get a box
started sliding across the floor.
• The magnitude of static friction force is:
f s  s FN
Magnitude of normal force
Coefficient of static friction
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Static friction
• When
f s  s FN
• Then the force applied to the
object from an external force is
equal to the static frictional force
and the object is just about to start
sliding.
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Coefficients of friction
• The coefficients of friction, both static
and kinetic, have no units.
• The coefficients of friction must be less
than 1.
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Example
• A 52-N sled is pulled across a cement
sidewalk at constant speed. A
horizontal force of 36 N is exerted.
What is the coefficient of kinetic friction
between the sidewalk and the metal
runners of the sled?
• 0.69
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On your own
• The sled from the example is now on
packed snow. The coefficient of friction
is 0.12. If a person weighing 650 N sits
on the sled, what force is needed to
slide the sled across the snow at a
constant speed?
• 84 N
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Example
• A runaway baby buggy is sliding without
friction across a frozen pond toward a hole in
the ice. You race after the buggy on skates.
As you grab it, you and the buggy are moving
toward the hole at speed v0. The coefficient
of friction between your skates and the ice as
you turn out the blades to brake is k. D is
the distance to the hole when you reach the
buggy, M is the mass of the buggy, and m is
your mass.
• What is the lowest value of D such that you
stop the buggy before it reaches the hole in
the ice?
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Equilibrium
•
•
•
•
When the net force on a particle is zero
The particle is in equilibrium.
It has a constant velocity.
It has zero acceleration.
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Example
• A 100-N body is shown suspended from
a system of cords. What is the tension
in the horizontal cord?
45
90
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On your own
• A traffic light is supported by two wires
as shown below. Which wire has the
greatest tension?
60
Wire 1
60
Wire 2
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Example
• A skier of mass 65.0 kg is pulled up a
snow-covered slope at constant speed
by a tow rope that is parallel to the
ground. The ground slopes upward at
a constant angle of 26° above the
horizontal and you can ignore friction.
Calculate the tension in the tow rope.
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On your own
• A man is dragging a trunk up the loading
ramp of a mover’s truck. The ramp has a
slope angle of 20.0° and the man pulls
upward with force F whose direction makes
an angle of 30.0° with the ramp.
• How large a force F is required in order for
the component Fx parallel to the ramp to be
28.0 N?
• How large will the component Fy then be?
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Example – inclined plane
• A 20-kg box rests on a frictionless ramp
with a 15° slope. A mover pulls up on a
rope attached to the box to pull it up
the incline. If the rope makes an angle
of 40° with the horizontal, what is the
force the mover must exert on the box
to give it an acceleration of 1 m/s2?
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On your own
• The system shown below is in
equilibrium, the incline is frictionless,
and the pulley is massless and
frictionless. What is the mass m?
m
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
40
3.5
kg
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Example
• Two children sitting on a sled at rest in the
snow ask you to pull them. You oblige by
pulling on the sled’s rope, which makes an
angle of 40° with the horizontal. The
children and sled have a combined mass of
50 kg. The coefficients of friction are
s = 0.2 and k = 0.15. Find the
acceleration of the sled and children, if the
tension in the rope is
– A) 100 N
– B) 140 N
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On your own
• A 5-kg block is held at rest against a
vertical wall by a horizontal force. What
is the minimum horizontal force needed
to prevent the block from falling if the
coefficient of friction between the wall
and the block is s=0.40?
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