Download Work (W) done by a constant force F exerted on an object through

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WORK – ENERGY - SUMMARY
♥ Work done by a constant force F exerted on an object through distance d is:
W = Fd cos Ѳ
(Fd = F cos Ѳ)
♥ Work done by a varying force F - graphically
The area under a Force - distance graph equals
the work done by that force
♦ Work done by force F is
positive
negative
• when the force and direction of
motion are generally in the
same directions (cos θ = +)
• when the force and direction of
motion are generally in the
opposite directions (cos θ = – )
• the force helps the motion
• force opposes the motion
maximum work
minimum work
W = Fd
W = – Fd
(the work done by friction force is always negative)
♦
Work done by force F is zero if:
• the force is exerted but
no motion is involved:
d = 0, W = 0
0
• the force is perpendicular to the direction of motion (cos 90 = 0)
for example
work done by normal
force can be zero
normal force is
perpendicular to v
W=0
normal force is
parallel to v
W = Fd = mgh
the work done by centripetal force is zero
Wnet = 0 → Wnet = ∆KE
→ no change in KE
no change in speed;
centripetal force can not
change the speed, only
direction
for example, gravitational
force on the moon does not
change speed of the moon
♥ Spring force/ Hooke’s law: F = – kx
The spring force is the force exerted by a compressed or stretched spring upon any object that is attached to it.
x is the displacement (extension/compression) of the spring's end from its
equilibrium position
F is the spring force exerted by the spring
k is a constant called spring constant (in SI units: N/m).
♥ Gravitational Potential energy, PE = mgh
What minimum force is needed to lift up an object to height h? F = mg
How much work is done by applied force in lifting it up height h? W = Fd = mgh
That work is now stored as PE in the object: PE = mgh.
So, if a force is lifting up an object along incline or climbing up the stairs, work done by applied force is still mgh.
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♥ Elastic Potential energy, EPE = ½ k x
What minimum force is needed to stretch/compress a spring (k) by extension x? F = kx
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How much work is done by applied force in stretching/compressing the spring by extension x? W = ½ kx
2
That work is now stored as EPE in the spring: EPE = = ½ kx .
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Work done by an applied force F = kx when extending a spring from extension x1 to x2 is: 𝑊𝑊 = 𝑘𝑘(𝑥𝑥22 − 𝑥𝑥12 )
♥ Kinetic energy
2
2
KE = ½ mv
♥ Work – Kinetic energy relationship: work done by net force changes kinetic energy
2
2
W = ∆KE = KEf – KEi = ½ mv – ½ mu
W = Fd cos Ѳ
When the net force and direction of motion are in generally the same directions, work is positive and KE is increasing.
When the net force and direction of motion are in generally opposite directions, work is negative and KE is decreasing.
♥ Work done by applied force changes potential energy (when net force is zero, so there is no acceleration).
▪ work done by applied force on spring is stored as elastic potential energy in the spring
▪ work done by applied force when lifting an object is stored as gravitational potential energy.
♥ Work done by net force changes kinetic energy (net force gives acceleration, therefore can change speed).
♥ Conservation of energy law
For the system that has only mechanical energy (ME = PE + KE)
and there is no frictional force acting on it, so no mechanical energy
is converted into heat, mechanical energy is conserved
ME1 = ME2 = ME3 = ME4
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2
mgh1 + ½ mv1 = mgh2 + ½ mv2 = • • • • • •
♥ Conservation of energy law with friction included
Friction converts part of kinetic energy of the object into heat energy. We say that the frictional force has dissipated energy.
This energy equals to the work done by the friction and it doesn’t belong to the object alone but is shared with environment.
ME1 – Ffr d = ME2
(Wfr = – Ffr d)
♥ Power is the work done in unit time or energy converted in unit time 𝑷𝑷 =
P=
𝑾𝑾
𝒕𝒕
or 𝑷𝑷 =
𝑬𝑬
measures how fast work is done or how quickly energy is converted. Power is a scalar quantity.
♦
𝒕𝒕
W
t
or P =
(1 W(Watt) = 1 J/ 1s)
There is another way to calculate power P = F v
● Back to collisions
◘ In all collisions and explosions momentum is conserved. In collisions some of KE is usually converted into heat and other
forms of energy; the system has less KE after collision. In explosions KE increases if there is an input of energy from a fuel or
explosive material.
◘
In an inelastic collision momentum is conserved but KE is not conserved.
Perfectly inelastic collision: the most of KE is converted into other forms of energy when objects after collision
stick together.
◘
In an elastic collision both momentum and kinetic energy are conserved. That means no energy is converted into heat.
◘ In the real world energy is always converted during a collision. However, some collisions are approximately elastic. The
collision of two pool balls is very nearly elastic, as is the collision between two steel ball bearings. In microscopic world there
are a lot of elastic collisions.
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