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Transcript
Fundamental Forces
• We have talked about a lot of different kinds of forces.
• Gravitational, friction, normal, fluid resistance, tension…
• Are these all actually different in nature?
• Four fundamental forces (we think):
• Gravitational
• Electromagnetic
• Strong
• Weak
• All interactions arise through one of these fundamental
forces.
• All of the interactions we have dealt with so far were
electromagnetic or gravitational.
Chapter 5 Summary
Applying Newton’s Laws
• Statics:
𝑭=0
• Dynamics:
𝑭 = 𝑚𝒂
• Friction
• Kinetic friction: 𝑓k = 𝜇k 𝑛
• Static friction: 𝑓s ≤ 𝜇s 𝑛
• Rolling resistance: 𝑓r = 𝜇r 𝑛
• Fluid resistance: 𝑓 = 𝑘𝑣 or 𝑓 = 𝐷𝑣 2
• Terminal velocity: 𝑣𝑡 =
• Circular Motion
• Fundamental forces
𝑚𝑔
𝐷
Chapter 6 Outline
Work and Kinetic Energy
• Work and energy
• Conservation of energy
• Kinetic Energy
• Work-energy theorem
• Work with varying forces
• Power
• Fundamental forces
Work and Kinetic Energy
• In everyday conversation, work would be any activity that
requires some effort.
• In physics, work is something that is done to change the
energy of an object.
• Energy can take many forms.
• Consider the case of applying a force on a body.
• As we saw last chapter, the body will accelerate.
• Its kinetic energy, or energy of motion, will increase.
• If we apply the force over a longer distance, we increase the
kinetic energy more.
Work and Forces
• If we apply a constant force,
𝐹, over some distance 𝑠, in
the same direction as the
force, the work done is:
𝑊 = 𝐹𝑠
• What are the units for work?
• Force is measured in newtons,
and distance in meters.
• Work is therefore measured in
newton-meters.
• We call this a joule.
• 1J= 1N∙m
Work and Forces Not Aligned with Displacement
• If the force is not applied in the same direction as the
displacement, only the component of the force aligned
with the displacement contributes to the work done.
• We only consider the component of the force parallel to the
displacement multiplied with the magnitude of the displacement.
• This is simply the dot product of the force and the displacement.
𝑊 = 𝑭 ∙ 𝒔 = 𝐹𝑠 cos 𝜙
Sign of Work
• Work is a scalar. It does not indicate a direction, but its
sign is still quite important.
• The sign of the work done on an object depends on the
direction of both the force and the displacement.
• If the force and the displacement are in the same direction, the
work done by the force on the body is positive.
• It is crucially important to indicate who/what is doing the work
and who/what the work is done upon.
Total Work
• In general, there are often more than one force acting on
an object.
• The total work done on the object depends on the net force
and the displacement of the object.
• Multiple forces/bodies can do different, sometimes opposing,
amounts of work on the body.
Work Example
Kinetic Energy
• When a force is applied to a body, it causes an
acceleration.
• A force applied over a distance, as we have said is the
definition of work.
• This changes the kinetic energy of the object.
• How can we relate work done to change in kinetic energy?
Kinetic Energy
• When a force is applied to a body, it causes an
acceleration.
• A force applied over a distance, as we have said is the
definition of work.
• This changes the kinetic energy of the object.
• How can we relate work done to change in kinetic energy?
Work-Energy Theorem
• Kinetic energy is:
𝐾 = 12𝑚𝑣 2
• The net work done on a body is equal to the change in
kinetic energy.
• This is the work-energy theorem.
𝑊tot = 𝐾2 − 𝐾1 = Δ𝐾
Work-Energy Example