Chapter 5 Work and Energy. 6-1 Work Done by a Constant Force The work done by a constant force is...
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Transcript of Chapter 5 Work and Energy. 6-1 Work Done by a Constant Force The work done by a constant force is...
Chapter 5
Work and Energy
6-1 Work Done by a Constant ForceThe work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:
(6-1)
6-1 Work Done by a Constant Force
In the SI system, the units of work are joules:
For person walking at constant velocity:
•Force and displacement are orthogonal, therefore the person does no work on the grocery bag
•Is this true if the person begins to accelerate?
Example 6-1. A 50-kg crate is pulled along a floor. Fp=100N and Ffr=50N. A) Find the work done by each force acting on th crateB)Find the net work done on the crate when it is dragged 40m.
Wnet = Wg + Wn + Wpy + Wpx + Wfr
Mechanical Energy
Types of Mechanical Energy
•Kinetic Energy = ½ mv2
•Potential Energy (gravitational) = mgh
•Potential Energy (stored in springs) = ½ kx2
6-3 Kinetic Energy, and the Work-Energy Principle
Wnet = Fnetd
but Fnet = ma
Wnet = mad
v22 = v1
2 + 2ad
a = v22 - v1
2 2dWnet = m (v2
2 - v12)
2We define the kinetic energy:
6-3 Kinetic Energy, and the Work-Energy Principle
The work done on an object is equal to the change in the kinetic energy:
• If the net work is positive, the kinetic energy increases.
• If the net work is negative, the kinetic energy decreases.
(6-4)
Example: A 145g baseball is accelrated from rest to 25m/s.A) What is its KE when released?B) What is the work done on the ball?
Potential Energy
• Potential energy is associated with the position of the object within some system
• Gravitational Potential Energy is the energy associated with the position of an object to the Earth’s surface
6-4 Potential Energy
In raising a mass m to a height h, the work done by the external force is
We therefore define the gravitational potential energy:
(6-5a)
(6-6)
6-4 Potential Energy
Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy.
6-4 Potential Energy
The force required to compress or stretch a spring is:
where k is called the spring constant, and needs to be measured for each spring. k is measured in N/m.
(6-8)
Conservation of Energy
• Energy cannot be created or destroyed• In the absence of non-conservative forces
such as friction and air resistance:
Ei = Ef = constant
• E is the total mechanical energy
fsgisg )PEPEKE()PEPEKE(
Example: A marble having a mass of 0.15 kg rolls along the path shown below. A) Calculate the Potential Energy of the marble at A (v=0)B) Calculate the velocity of the marble at B.C) Calculate the velocity of the marble at C
A
C
B
10m
3m
Ex. 6-11 Dart Gunmdart = 0.1kgk = 250n/mx = 6cmFind the velocity of the dart when it releases from the spring at x = 0.
A marble having a mass of 0.2 kg is placed against a compressed spring as shown below. The spring is initially compressed 0.1m and has a spring constant of 200N/m. The spring is released. Calculate the height that the marble rises above its starting point. Assume the ramp is frictionless.
h
Nonconservative Forces
• A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points.
• Examples of nonconservative forces– kinetic friction, air drag, propulsive forces
• Examples of conservative forces– Gravitational, elastic, electric
Power• Often also interested in the rate at which the
energy transfer takes place• Power is defined as this rate of energy transfer
– SI units are Watts (W)
2
2
s
mkg
s
JW
P = W = FΔx = Fvavg
t t
Power, cont.
• US Customary units are generally hp– need a conversion factor
– Can define units of work or energy in terms of units of power:
• kilowatt hours (kWh) are often used in electric bills
W746s
lbft550hp1