Topics 10 and 11. Work, Power, and Energy

Topics 10 and 11. Work, Power, and Energy

Topic 10: Work, Power, and Simple Machines

1. Work

2. Work and the Direction of Force

3. Power

4. Simple Machines

5. Mechanical Advantage

Notes should include:

Work: Whenever you exert a force and cause an object to move you are doing work. For example, if you push a piece of furniture across a room, you are doing work. On the other hand, let us suppose that you push on a wall real hard for a long enough time that you feel fatigue because of your effort, but the wall does not move. Have you done any work? No you have not. Work is the product of the unbalanced force acting on an object and the displacement of the object due to that force. The equation for work is W = F d. The unit for work is the joule (J) which is equal to 1 Newton meter ( N m ).

Work and Direction of Force: When you push a lawn mower or pull a wagon, you notice that the handle is not parallel to the ground. This means that not all the net force (the unbalanced force) is going towards moving the object. Only the horizontal component contributes to the motion of the object. The portion of the force that is the vertical component of the net force contributes nothing to the movement of the object across the ground. The vertical component would be canceled (balanced) by the upward resisting force of the ground in the case of the lawn mower.

The equation for finding the work done when only the horizontal component of the force is contributing to the work, is W = F (cos ) d or W = F d (cos ).

Power: Power is a measurement of the rate at which work is done. The equation for power tells us that power equals work divided by time. That is, P = W / t. The unit for power is the watt. The symbol for the unit watt is an upper case W. You should be careful to avoid the confusion that can arise with the letter w being used as a symbol in several different circumstances. One watt of power is equal to 1 J / s.

Simple Machines: Essentially all mechanically based machines are made up of one or more of the six simple machines. The six simple machines are the lever, the inclined plane, the wedge, the screw, the pulley, and the wheel and axle. With any of the simple machines the work done on the machine (i.e. moving the end of a lever) is called the input work, while the work done by the machine (i.e. the heavy object moves, or the lid comes off of a jar, etc.) is called the output work.

Mechanical Advantage: Theoretically we can discuss the output work being equal to the input work. This would be an ideal situation where you would have an ideal machine. The input work would equal a force, called the effort force, multiplied by the displacement this force produces. For example, in the case of a lever. Your effort force acting on one end of the lever causes that end to move. The output work is the product of the force that the machine exerts, called the resistance force, and the displacement this force produces. In the example of the lever the other end of the lever from your hand exerts a force against some object. It is this force and the displacement of the object multiplied together that gives you the value for the output work. In the form of equations, what we are saying here can be written as Wi = Wo and if the variables for calculating work are substituted in for the work values it becomes Fe de = Fr dr.

If the above equation is rearranged, you can obtain two ratios equal to one another. The equation would look like Fr / Fe = de / dr. The left side of this equation has a ratio called the mechanical advantage. The right side of the equation has a ratio called the ideal mechanical advantage. The mechanical advantage tells you the amount that the machine has increased the effort force. The ideal mechanical advantage tells you the maximum value you could have, if no other forces were to interfere such as friction. In the real world with very real machines, the MA is always going to be less than the IMA. Since, no machine in the real world will operate at ideal conditions (100 % efficiency), you need to use an equation to determine the degree of efficiency at which the machine is operating. There are two equations, which you can use to find the percent efficiency of a machine. One is eff = Wo / Wi x 100%, the other is eff = (MA / IMA) x 100%. (remember that multiplying a ratio by 100% converts the ratio from a decimal value to a percentage value)

Topic 11: Energy, GPE and KE

1. Energy, A More Meaningful View of Work

2. Potential Energy and Base Levels

3. Work and Change in Potential Energy

4. Kinetic Energy

5. Conservation of Energy

6. Elastic and Inelastic Collisions

Notes should include:

Energy, A More Meaningful View of Work: Work is a measure of the change in energy as in a situation where it is apparent that energy is transferred. For example, when you push a piece of furniture across the floor, you are transferring some of the chemical energy you have acquired from ingesting food to the desk floor system resulting in the movement of the desk with respect to the floor. It wouldn't be very practical to try to measure the energy change by measuring the energy of the system before and after the change occurs and then subtracting. The practical means of determining the energy change that occurs in a system is to determine the work done.

In working with a situation where there is a change in energy (energy is transferred) You need to work with the terms potential and kinetic energy. Potential Energy is the energy an object has with respect to a reference point. In a sense it is stored energy. For example, a mass placed 10 m above the ground has more gravitational potential energy than the same mass placed 1 m above the ground. Kinetic Energy is the energy an object has because of its motion. For example, a car standing at a traffic light (stationary with respect to the ground) has zero kinetic energy, while the same car moving at 30 km/h along a street (movement with respect to the ground) has kinetic energy. Energy is measured in terms of work done and like work is measured using the unit the Joule. Like work, energy is a scalar quantity.

Potential Energy and Base Levels: As suggested in an earlier example, gravitational potential energy depends on the position of the object with respect to the earth. An object at some distance above the earth's surface has the capacity to do work as in the case of a pile driver, which is used to drive very large wooden or steel posts into the ground. In such a situation the earth's surface is the base level or reference point. The reference point, called the base level, is a point selected to be the position assigned zero potential energy.

Work and Change in Potential Energy: Work is the product of force and displacement, as expressed in the equation, W = F d. The change in potential energy is equal to work done to produce that change. The equation is /\PE = W = F d. When working with gravitational potential energy the change in potential energy equation can be written as /\PE = mgh. It follows that the equation could be written as W = /\PE = PEf - PEi = F d.

Kinetic Energy: Kinetic energy is the energy an object has because its mass is in motion. If an object is stationary with respect to the selected reference point, it has zero kinetic energy (0 J). The equation for kinetic energy is KE = 0.5 m v2. Since work is equal to the change in energy, we can also write the equation W = /\KE = KEf - KEi = 0.5 m vf2 - 0.5 m vi2.

Conservation of Energy: When work is done on a system, the energy will change form. For example, consider a simple roller coaster with a series of hills. When the roller coaster is at the top of the first hill it has potential energy. As it moves down the hill the potential energy decreases and the kinetic energy increases and the speed of the cars increase. At the bottom of the hill, the roller coaster has had the potential energy become kinetic energy. Then as it continues up the same hill, the kinetic energy changes back to potential energy as the speed of the cars slows. In an example such as dropping a ball you can see the potential energy changing to kinetic energy. A very useful equation for this circumstance is /\PE = /\KE. Another way to write this equation is PEi + KEi = PEf + KEf.

Kinetic Energy, Elastic and Inelastic Collisions: In an elastic collision, the total kinetic energy before and after the collision remains the same. If any decrease in kinetic energy occurs it is accounted for by an increase in the thermal energy of the objects themselves. In an inelastic collision, the kinetic energy is not conserved. This occurs because the masses in the collision combine and move off with a single velocity.

Vocabulary: Energy, Kinetic Energy, Work, Work-Energy Theorem, Joule, Power, Watt, machine, Effort Force, Resistance Force, Mechanical Advantage, Ideal Mechanical Advantage, Efficiency, Compound Machine, Gravitational Potential Energy, Reference Level, Elastic Potential Energy, Law of Conservation of Energy, Mechanical Energy.

Skills to be learned:

Solve problems involving Work

Solve problems involving Work and the Direction of Force

Solve problems involving Power

Identify the six Simple Machines

Solve problems involving Mechanical Advantage

Solve Work and Change in Potential Energy Problems

Solve Kinetic Energy Problems

Solve Conservation of Energy Problems

Assignments:

Practice Problem Set(s) Textbook references, TBA

Exercise(s) 10-1, 10-2, 10-3, 10-4, 11-1 and 11-2

Activities TBA

Resources:

This handout and the Overhead and Board Notes discussed in class

Textbook: Chapters 10 and 11

WB Lessons and Problem Sets

- “Study Of Work, Power, …, and Energy”

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