PHYS 100 Chapter Notes - Chapter 7: Chemical Energy, Solar Cell, Radian
10 May 2018
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Chapter 7
Work
- The scientific definition of work differs in some way from its meaning
o Reveals its relationship to energy
o Whenever work is done, energy is transferred
o Work done on a system by a constant force is designed to be the product of the
component of the force in the direction of motion times the direction through
which the force acts
▪ W = Fd cosθ
• W is work
• D is displacement
• θ is the angle between force Vector (F) and Displacement vector
(D)
o The work done on a system by a constant force is the product of the component of
the force in the direction of motion times the distance through which the force
acts
▪ This is expressed in equation form as
• W = Fd cos θ
- Calculating work
o Work and energy have the same units
o Force times distance, work and energy are measured in newton-meters
▪ Newton meter is given the special name, joule (J)
▪ 1 J = 1N per m = 1kg per m2s2
o Example
▪ How much work is done on a lawn mower if the person exterts 75N of
force at 35 degrees below the horizontal and pushes the mower 25m
• W = Fd cosθ
o Force = 75N
o Distance = 25m
o Cosθ = cos35
• W = 75N(25m)(Cos35)
o 1536J
o 1.54x103J
Kinetic Energy and the Work Energy Theorem
- Net force causes acceleration
- Net work is defined to be the sum of the work done by all external forces
o Net work is the work done by the net external force (FNet)
▪ WNet = FNetDcosθ
• θ is the angle between force vector and displacement vector
• FCosθ is constant
• Area under the curve represents the work done by the force
▪ The force of gravity and the normal force acting on a package are
perpendicular and do not work
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▪ Equal in magnitude and opposite in direction so they cancel in calculating
net force
• Net Force arises from the horizontal applied for (FApp) to accelerate
the package from V0 to V
▪ The kinetic energy of the package increases, indicating that the net work
done on the system is positive
• FNet = ma
• Wnet = mad
▪ To get the relationship between net work and speed given to a system by
the net force acting on it
• Take D = x-x0 and use the equation for the change in speed over a
distance if the acceleration has a constant value
o V2 = V02+2ad
o This is called the work-energy theorem, and it implies that
the net work on a system equals the change in the quantity
½ mv2
o The quantity ½ mv2 in the work energy theorem is defined
to be translational Kinetic Energy (KE) of a mass (m)
moving at a speed (V)
▪ KE = ½ MV2
▪ Example: a 30kg package is moving at .5m/s
• KE = ½ mv2
o M = 30kg
o V = 0.500m/s
o KE = ½ (30kg)(0.500m/s)2
▪ 3.75kg/m2/s2
▪ 3.75J
▪ Example: Push on a 30kg package with a force of 120N through a distance
of 0.800m and opposing friction force of 5N
• Calculate net work
o FNet = 120N – 5N = 115N
o WNet = FNetD
▪ FNet = 115N
▪ D = 0.800m
▪ 115N(0.800m) = 92J
• Calculate Applied Force
o WApp = FAppD
▪ (120N)(0.800m)
• 96J
• Work by Friction
o WFr = -FFrD
▪ -5N(0.800m)
▪ -4J
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Gravitational Potential Energy
Work Done Against Gravity
- Work done against the gravitational force goes into an important form of stored energy
o Work done in lifting an object of mass (m) through a height (h)
o If the object is lifted up at a constant speed, then the force needed to lift it is equal
to its weight (mg)
▪ The work done on the mass is then W = Fd = mgh
• This is defined to be gravitational potential Energy (PEg)
• Potential energy is a property of a system rather than of a single
object
▪ PE = (m)(g)(h)
- Converting between potential and Kinetic Energy
o Gravitational potential energy may be converted to other forms of energy, such as
kinetic energy
▪ If we release the mass, gravitational force will do an amount of work equal
to mgh on it
• Increasing kinetic energy by the same amount
• The change in gravitational potential energy is defined as
o ΔPEg =mgh,
• Example: If a 0.500kg mass hung from a clock is raised 1m
o Mgh = ?
o m = .5kg
o g = 9.80m/s2
o h = 1m
o (0.500kg)(9.8m/s2)(1m)
▪ 4.9J
- Using potential energy to simplify calculations
o Any change in vertical position (h) of a mass (m) is accompanied by a change in
gravitational potential energy
▪ Example: A 60kg person jumps onto the floor from a height of 3m. Knee
joints compressing by 0.5cm
• -FD = mgh
o F = -mgh/d
▪ -(60kg)(9.80m/s2)(-3m)/5x10-3
▪ 3.53x105N
Conservative Forces and Potential Energy
- A conservative force is one, depends only on the starting and ending points of a motion
and not on the path taken
- Potential energy is defined as any conservative force, just as we did for the gravitational
force. Energy that can be used to do work
o Stored energy is recoverable as work
- Potential energy of a spring – Hooke’s Law
o (PEs)
o F = kx
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Document Summary
2+2ad: this is called the work-energy theorem, and it implies that the net work on a system equals the change in the quantity. Converting between potential and kinetic energy: gravitational potential energy may be converted to other forms of energy, such as kinetic energy. If we release the mass, gravitational force will do an amount of work equal to mgh on it. A conservative force is one, depends only on the starting and ending points of a motion and not on the path taken. Potential energy is defined as any conservative force, just as we did for the gravitational force. Energy that can be used to do work: stored energy is recoverable as work. Conservation of mechanical energy: kei + pei = kef + pef. I and f are initial and final values. Spring is compressed 4m and has force constant of 250n/m: find how fast the car is going before it starts up the slope, kxi.
