1. What is the relevance of Physics in day to day activities?
2. How importance is understanding Physics?
3. If you are traveling in an airplane and dropped a ball where will it hit? why?
4. A large rock is dropped from a bridge into the river below.
a) if the time required to fall is 1.7 seconds, with what velocity, in m/sec, does it hit the water? b) what is the height, in meters, of the bridge above the water?
5. A car possesses 20 000 units of momentum. What would be the car's new momentum if its velocity were doubled.
6. Find the height (in m) from which you would have to drop your textbook so that it would have a speed of 14.2 m/s just before it hits the floor?
7. Differentiate work from power
8. What can make any work be more efficient?
9. If the population of the U.S. was 200,000,000, what was the average rate of energy consumption per person?
Tuesday, March 11, 2008
Tuesday, February 26, 2008
announcements
MARCH 2 and 9 deadlines i will be at the school for any clarifications
MARCH 16 - Finals first part
MARCH 23- Part II finals
MARCH 16 - Finals first part
MARCH 23- Part II finals
march 2
| If you push vigorously against a brick wall, how much work do you do on the wall? |
A person pushes a 10 kg cart a distance of 20 meters by exerting a 60 Newton horizontal force. The frictional resistance force is 50 Newtons. How much work is done by each force acting ont he cart? How much kinetic energy does the cart have at the end of the 20 meters if it started from rest:
An automobile of mass 1200 kg has a speed of 30 m/s on a horizontal road when the engine is developing 37300 Watts (50.0 horsepower). What is the speed, with the same power output, if the automobile now climbs a hill inclined at 30o?
In the early 1980's, the total consumption of electrical energy in the U.S. was on the order of 1 X 1019 joules per year.
a) What was the average rate of energy consumption in watts? kilowatts?
b) If the population of the U.S. was 200,000,000, what was the average rate of energy consumption per person?
c) If the sun transfers energy to the earth by radiation at a rate of 1.4 kW per square meter of surface, how great an area would be required to collect the energy cited above?
The human heart is a powerful and reliable pump. Each 24 hour day, it takes in and discharges over 7500 liters of blood. If the work done by the heart is equal to the work required to lift this amount of blood a height equal to the average American female (1.63 m), and if the density of blood is the same as that of water,
a) how much work does the heart do in a day?
b) what is the power output in watts? horsepower?
example of power
Problem 3.1:
An elevator must lift 1000 kg a distance of 100 m at a velocity of 4 m/s. What is the average power the elevator exerts during this trip?
Solution for Problem 3.1
The work done by the elevator over the 100 meters is easily calculable: W = mgh = (1000)(9.8)(100) = 9.8×105 Joules. The total time of the trip can be calculated from the velocity of the elevator: t = 25 s. Thus the average power is given by: P == 3.9×104 Watts, or 39 kW.
An elevator must lift 1000 kg a distance of 100 m at a velocity of 4 m/s. What is the average power the elevator exerts during this trip?
Solution for Problem 3.1
The work done by the elevator over the 100 meters is easily calculable: W = mgh = (1000)(9.8)(100) = 9.8×105 Joules. The total time of the trip can be calculated from the velocity of the elevator: t = 25 s. Thus the average power is given by: P == 3.9×104 Watts, or 39 kW.
power
Power
Mechanical systems, an engine for example, are not limited by the amount of work they can do, but rather by the rate at which they can perform the work. This quantity, the rate at which work is done, is defined as power.
Equations for Power
From this very simple definition, we can come up with a simple equation for the average power of a system. If the system does an amount of work, W, over a period of time, T, then the average power is simply given by:
=
It is important to remember that this equation gives the average power over a given time, not the instantaneous power. Remember, because in the equation w increases with x, even if a constant force is exerted, the work done by the force increases with displacement, meaning the power is not constant. To find the instantaneous power, we must use calculus:
P =
In the sense of this second equation for power, power is the rate of change of the work done by the system.
From this equation, we can derive another equation for instantaneous power that does not rely on calculus. Given a force that acts at an angle θ to the displacement of the particle,
P = = = F cosθ
Since = v ,
P = Fv cosθ
Though the calculus is not necessarily important to remember, the final equation is quite valuable. We now have two simple, numerical equations for both the average and instantaneous power of a system. Note, in analyzing this equation, we can see that if the force is parallel to the velocity of the particle, then the power delivered is simply P = Fv.
Units of Power
The unit of power is the joule per second, which is more commonly called a watt. Another unit commonly used to measure power, especially in everyday situations, is the horsepower, which is equivalent to about 746 Watts. The rate at which our automobiles do work is measured in horsepower.
Power, unlike work or energy, is not really a "building block" for further studies in physics. We do not derive other concepts from our understanding of power. It is far more applicable for practical use with machinery that delivers force. That said, power remains an important and useful concept in classical mechanics, and often comes up in physics courses.
Mechanical systems, an engine for example, are not limited by the amount of work they can do, but rather by the rate at which they can perform the work. This quantity, the rate at which work is done, is defined as power.
Equations for Power
From this very simple definition, we can come up with a simple equation for the average power of a system. If the system does an amount of work, W, over a period of time, T, then the average power is simply given by:
=
It is important to remember that this equation gives the average power over a given time, not the instantaneous power. Remember, because in the equation w increases with x, even if a constant force is exerted, the work done by the force increases with displacement, meaning the power is not constant. To find the instantaneous power, we must use calculus:
P =
In the sense of this second equation for power, power is the rate of change of the work done by the system.
From this equation, we can derive another equation for instantaneous power that does not rely on calculus. Given a force that acts at an angle θ to the displacement of the particle,
P = = = F cosθ
Since = v ,
P = Fv cosθ
Though the calculus is not necessarily important to remember, the final equation is quite valuable. We now have two simple, numerical equations for both the average and instantaneous power of a system. Note, in analyzing this equation, we can see that if the force is parallel to the velocity of the particle, then the power delivered is simply P = Fv.
Units of Power
The unit of power is the joule per second, which is more commonly called a watt. Another unit commonly used to measure power, especially in everyday situations, is the horsepower, which is equivalent to about 746 Watts. The rate at which our automobiles do work is measured in horsepower.
Power, unlike work or energy, is not really a "building block" for further studies in physics. We do not derive other concepts from our understanding of power. It is far more applicable for practical use with machinery that delivers force. That said, power remains an important and useful concept in classical mechanics, and often comes up in physics courses.
examples
Problem 1.1:
A 10 kg object experiences a horizontal force which causes it to accelerate at 5 m/s2, moving it a distance of 20 m, horizontally. How much work is done by the force? \
The magnitude of the force is given by F = ma = (10)(5) = 50 N. It acts over a distance of 20 m, in the same direction as the displacement of the object, implying that the total work done by the force is given by W = Fx = (50)(20) = 1000 Joules.
A 10 kg object experiences a horizontal force which causes it to accelerate at 5 m/s2, moving it a distance of 20 m, horizontally. How much work is done by the force? \
The magnitude of the force is given by F = ma = (10)(5) = 50 N. It acts over a distance of 20 m, in the same direction as the displacement of the object, implying that the total work done by the force is given by W = Fx = (50)(20) = 1000 Joules.
work
Definition of Work
Work, though easily defined mathematically, takes some explanation to grasp conceptually. In order to build an understanding of the concept, we begin with the most simple situation, then generalize to come up with the common formula.
The Simple Case
Consider a particle moving in a straight line that is acted on by a constant force in the same direction as the motion of the particle. In this very simple case, the work is defined as the product of the force and the displacement of the particle. Unlike a situation in which you hold something in place, exerting a normal force, the crucial aspect to the concept of work is that it defines a constant force applied over a distance. If a force F acts on a particle over a distance x, then the work done is simply:
W = Fx
Since w increases as x increases, given a constant force, the greater the distance during which that force acts on the particle, the more work is done. We can also see from this equation that work is a scalar quantity, rather than a vector one. Work is the product of the magnitudes of the force and the displacement, and direction is not taken into account.
What are the units of work? The work done by moving a 1 kg body a distance of 1 m is defined as a Joule. A joule, in terms of fundamental units, is easily calculated:
W = Fx = (m) =
The joule is a multipurpose unit. It serves not only as a unit of work, but also of energy. Also, the joule is used beyond the realm of physics, in chemistry, or any other subject dealing with energy.
In dynamics we were able to define a force conceptually as a push or a pull. Such a concise definition is difficult to generate when dealing with work. To give a vague idea, we can describe work as a force applied over a distance. If a force is to do work, it must act on a particle while it moves; it cannot just cause it to move. For instance, when you kick a soccer ball, you do no work on the ball. Though you produce a great deal of motion, you have only instantaneous contact with the ball, and can do no work. On the other hand, if I pick the ball up and run with it, I do work on the ball: I am exerting a force over a certain distance. In technical jargon, the "point of application" of the force must move in order to do work.
Work, though easily defined mathematically, takes some explanation to grasp conceptually. In order to build an understanding of the concept, we begin with the most simple situation, then generalize to come up with the common formula.
The Simple Case
Consider a particle moving in a straight line that is acted on by a constant force in the same direction as the motion of the particle. In this very simple case, the work is defined as the product of the force and the displacement of the particle. Unlike a situation in which you hold something in place, exerting a normal force, the crucial aspect to the concept of work is that it defines a constant force applied over a distance. If a force F acts on a particle over a distance x, then the work done is simply:
W = Fx
Since w increases as x increases, given a constant force, the greater the distance during which that force acts on the particle, the more work is done. We can also see from this equation that work is a scalar quantity, rather than a vector one. Work is the product of the magnitudes of the force and the displacement, and direction is not taken into account.
What are the units of work? The work done by moving a 1 kg body a distance of 1 m is defined as a Joule. A joule, in terms of fundamental units, is easily calculated:
W = Fx = (m) =
The joule is a multipurpose unit. It serves not only as a unit of work, but also of energy. Also, the joule is used beyond the realm of physics, in chemistry, or any other subject dealing with energy.
In dynamics we were able to define a force conceptually as a push or a pull. Such a concise definition is difficult to generate when dealing with work. To give a vague idea, we can describe work as a force applied over a distance. If a force is to do work, it must act on a particle while it moves; it cannot just cause it to move. For instance, when you kick a soccer ball, you do no work on the ball. Though you produce a great deal of motion, you have only instantaneous contact with the ball, and can do no work. On the other hand, if I pick the ball up and run with it, I do work on the ball: I am exerting a force over a certain distance. In technical jargon, the "point of application" of the force must move in order to do work.
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