Transcript Work, Energy and Momentum

ICP
“Work, Energy and Momentum”
Core Content
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SC-HS-1.2.1
Students will: select or construct accurate and
appropriate representations for motion (visual,
graphical and mathematical); defend
conclusions/explanations about the motion of objects
and real-life phenomena from evidence/data.
Objects change their motion only when a net force is
applied. Newton’s Laws of motion are used to describe
the effects of forces on the motion of objects.
Conservation of mechanical energy and conservation of
momentum may also be used to predict motion. DOK 3
Work
work - the product of a net force and
the distance through which it acts
 work = force x distance
 W = Fd
 The unit for work is the joule, J.
 joule = newton x meter (J = Nm)
 joule - the amount of energy expended
when a 1N force acts through 1m
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Sample Problem
How much work is done on a vacuum
cleaner pulled 3.0m by a force of 50N
applied on the horizontal?
 W = Fd
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= 50N x 3m
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= 150 Nm
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= 150J
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Challenge!
An acceleration of 2 m/s2 acts on a 10kg
mass through a distance of 8m. How much
work is done?
 W = Fd
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= ma d
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= 10kg x 2 m/s2 x 8m
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= 160 Nm
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= 160J
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Energy
 Energy
is measured in terms of the work
it does or can do.
 Energy has the same units as work, SI joule.
 Like work, energy is a scalar quantity.
 Energy is either potential or kinetic.
 Potential energy (PE) - energy of position
 Kinetic energy (KE) - energy of motion
Kinetic Energy
F = ma
 F d = ma d
 F d = mv2/2
 KE = 1/2 mv2
 Sample Problem - Calculate the kinetic energy
of a 2kg object moving at 5 m/s.
 KE = 1/2mv2 = .5(2kg x (5 m/s)2)
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= 25kg m2/s2 = 25J
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Potential Energy
The increase in the potential energy of any
system is equal to the work done on the
system. Gravitational potential energy
depends on the mass and height of the object
in question.
 PE = Fd = mg d = mgh
 A 5.0 kg bowling ball is lifted to a height of
1.5m. What is its increase in potential energy?
 PE = mgh = 5kg x 9.8 m/s2 x 1.5m
= 73.5kg.m/s2.m = 73.5J
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Work, Energy, and Power
energy - the capacity to do work
 energy = work (same units)
 power - the time rate at which work is
done
P=W/t
 The SI unit for power is the watt.
 watt - the power required for 1 joule of
work to be done in 1 second
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Sample Problem
A machine produces 80N of force
through a distance of 10m. How much
work is done?
 W = Fd = 80N x 10m = 800 J
 If the work is done in 5 seconds, how
much power is used?
 P = W/t = 800J/5s = 160 J/s = 160 watts
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Momentum and Impulse
momentum - the product of the mass
of an object and its velocity
 unit for momentum.......kg m/s
 impulse - the product of a force and
the length of time during which it acts
 unit for impulse.............N s
 Using the units, find the relationship
between impulse and momentum.
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Newton’s Third Law of Motion
 Newton’s
Third Law of Motion
states that for every action there is
an equal and opposite reaction.
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Object A
Object B
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Ft
=
-Ft
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mv
=
-mv
Law of Conservation of
Momentum
 The
Law of Conservation of
Momentum states that the total
momentum of an isolated system
cannot change.
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mv before collision = mv after collision
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m1v1 + m2v2 = m1v’1 + m2v’2
Sample Problem
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A mass of 5.0g moves with a velocity of
20cm/s. This mass collides with a second
mass of 10g which is moving along the
same line with a velocity of 10cm/s. After
the collision, the 5.0g mass is moving at
8cm/s. What is the velocity of the 10g mass
after the collision?
Conservation of Matter and
Energy
The Law of Conservation of Matter and
Energy states “Matter and energy are
interchangeable and the total amount of
matter and energy in the universe remains
constant.
 E = mc2 (c = 3 X 108 m/s)
 Calculate the energy released when 5g
of mass is converted to energy.
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Open Response
Suppose you are in a canoe two feet
from a boat dock. If you want to get
out of the canoe, describe, using
Newton’s Laws of motion and any
vector diagrams you choose;
 A. The effect of jumping onto the ramp.
 B. The effect of stepping onto the ramp.
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