File Name: mechanics work energy and power .zip
Consider a particle of mass m moving linearly with an applied force F constantly acting on it.
This set of 32 problems targets your ability to use equations related to work and power, to calculate the kinetic, potential and total mechanical energy, and to use the work-energy relationship in order to determine the final speed, stopping distance or final height of an object.
The more difficult problems are color-coded as blue problems. Work results when a force acts upon an object to cause a displacement or a motion or, in some instances, to hinder a motion. Three variables are of importance in this definition - force, displacement, and the extent to which the force causes or hinders the displacement.
Each of these three variables find their way into the equation for work. That equation is:. The most complicated part of the work equation and work calculations is the meaning of the angle theta in the above equation. The angle is not just any stated angle in the problem; it is the angle between the F and the d vectors.
In solving work problems, one must always be aware of this definition - theta is the angle between the force and the displacement which it causes. If the force is in the same direction as the displacement, then the angle is 0 degrees. If the force is in the opposite direction as the displacement, then the angle is degrees.
If the force is up and the displacement is to the right, then the angle is 90 degrees. This is summarized in the graphic below. Power is defined as the rate at which work is done upon an object. Like all rate quantities, power is a time-based quantity.
Power is related to how fast a job is done. Two identical jobs or tasks can be done at different rates - one slowly or and one rapidly. The work is the same in each case since they are identical jobs but the power is different. The equation for power shows the importance of time:. Special attention should be taken so as not to confuse the unit Watt, abbreviated W, with the quantity work, also abbreviated by the letter W. Combining the equations for power and work can lead to a second equation for power.
If this equation is re-written as. Thus, the equation can be re-written as. A few of the problems in this set of problems will utilize this derived equation for power.
Potential energy is the stored energy of position. In this set of problems, we will be most concerned with the stored energy due to the vertical position of an object within Earth's gravitational field. Such energy is known as the gravitational potential energy PE grav and is calculated using the equation. Kinetic energy is defined as the energy possessed by an object due to its motion. An object must be moving to possess kinetic energy. The amount of kinetic energy KE possessed by a moving object is dependent upon mass and speed.
The equation for kinetic energy is. The total mechanical energy possessed by an object is the sum of its kinetic and potential energies. There is a relationship between work and total mechanical energy.
The relationship is best expressed by the equation. In words, this equations says that the initial amount of total mechanical energy TME i of a system is altered by the work which is done to it by non-conservative forces W nc.
The final amount of total mechanical energy TME f possessed by the system is equivalent to the initial amount of energy TME i plus the work done by these non-conservative forces W nc. The mechanical energy possessed by a system is the sum of the kinetic energy and the potential energy. Thus the above equation can be re-arranged to the form of. The work done to a system by non-conservative forces W nc can be described as either positive work or negative work.
Positive work is done on a system when the force doing the work acts in the direction of the motion of the object. Negative work is done when the force doing the work opposes the motion of the object. When a positive value for work is substituted into the work-energy equation above, the final amount of energy will be greater than the initial amount of energy; the system is said to have gained mechanical energy. When a negative value for work is substituted into the work-energy equation above, the final amount of energy will be less than the initial amount of energy; the system is said to have lost mechanical energy.
There are occasions in which the only forces doing work are conservative forces sometimes referred to as internal forces. Typically, such conservative forces include gravitational forces, elastic or spring forces, electrical forces and magnetic forces.
When the only forces doing work are conservative forces, then the W nc term in the equation above is zero. In such instances, the system is said to have conserved its mechanical energy. The proper approach to work-energy problem involves carefully reading the problem description and substituting values from it into the work-energy equation listed above. Inferences about certain terms will have to be made based on a conceptual understanding of kinetic and potential energy.
For instance, if the object is initially on the ground, then it can be inferred that the PE i is 0 and that term can be canceled from the work-energy equation.
In other instances, the height of the object is the same in the initial state as in the final state, so the PE i and the PE f terms are the same. As such, they can be mathematically canceled from each side of the equation.
In other instances, the speed is constant during the motion, so the KE i and KE f terms are the same and can thus be mathematically canceled from each side of the equation. Finally, there are instances in which the KE and or the PE terms are not stated; rather, the mass m , speed v , and height h is given. In such instances, the KE and PE terms can be determined using their respective equations. Make it your habit from the beginning to simply start with the work and energy equation, to cancel terms which are zero or unchanging, to substitute values of energy and work into the equation and to solve for the stated unknown.
An effective problem solver by habit approaches a physics problem in a manner that reflects a collection of disciplined habits. While not every effective problem solver employs the same approach, they all have habits which they share in common. These habits are described briefly here. An effective problem-solver The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.
Physics Tutorial. What Can Teachers Do Subscription Selection. The Calculator Pad.
Any force which conserves mechanical energy, as opposed to a nonconservative force. See statement of conservation of mechanical energy. Property of conservative forces which states that the work done on any path between two given points is the same. The energy of configuration of a conservative system. For formulae, see Definition of potential energy, gravitational potential energy, and Definition of potential energy given a position-dependent force.
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The principle of work and kinetic energy also known as the work-energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy. Kinetic Energy : A force does work on the block. The kinetic energy of the block increases as a result by the amount of work. This relationship is generalized in the work-energy theorem.
This set of 32 problems targets your ability to use equations related to work and power, to calculate the kinetic, potential and total mechanical energy, and to use the work-energy relationship in order to determine the final speed, stopping distance or final height of an object. The more difficult problems are color-coded as blue problems. Work results when a force acts upon an object to cause a displacement or a motion or, in some instances, to hinder a motion. Three variables are of importance in this definition - force, displacement, and the extent to which the force causes or hinders the displacement. Each of these three variables find their way into the equation for work.
Suppose a force F acts on a body, causing it to move in a particular direction. Work done is measured in joules which has symbol J. Now suppose that this force is at an angle of a to the horizontal. Now suppose that the force we are considering is one which causes a body to be lifted off of the ground.
Renatta Gass is out with her friends. Misfortune occurs and Renatta and her friends find themselves getting a work out. They apply a cumulative force of N to push the car m to the nearest fuel station.
Но потом поняла, куда смотрел коммандер: на человеческую фигуру шестью этажами ниже, которая то и дело возникала в разрывах пара. Вот она показалась опять, с нелепо скрюченными конечностями. В девяноста футах внизу, распростертый на острых лопастях главного генератора, лежал Фил Чатрукьян.
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