Work & Energy w/o Machines Level Physics

Definition of Work Work = Force x displacement Work is a scalar quantity equal to the product of the displacement d and the component of the force Fx in the direction of the displacement. Work = Force x displacement Work = Fx d

Work (Joules) Force, F Displacement, d In order to accomplish work on an object there must be a force exerted on the object and it must move parallel to the direction of the force. Force, F Displacement, d Which force is doing the work as she pulls the luggage?

When a force does no work A force with no motion or a force perpendicular to the motion does no work                                                                             Illustration: Nave. R. (2010)

Positive Work F d Force F contributes to displacement x. Example: If F = 40 N and d = 4 m, then Author: Tippens, P. (2007)

Negative Work d f The friction force f opposes the displacement. Example: If f = -10 N and d = 4 m, then Author: Tippens, P. (2007)

Resultant Work or Net Work Resultant work is the algebraic sum of the individual works of each force. F d f Example: F = 40 N, f = -10 N and d = 4 m Author: Tippens, P. (2007)

Resultant Work (Cont.) Resultant work is also equal to the work of the RESULTANT force. 40 N 4 m -10 N Example: Work = (F - f) d Author: Tippens, P. (2007)

Power = work / time Power = W / t Power is measured in watts = J / sec.                                             Time (sec) Another Unit for Energy = kilowatt-hour (kwh) Work (J) Power = F v (only if v is constant)

What power is consumed in lifting a 70-kg robber 1.6 m in 0.50 s? Example of Power What power is consumed in lifting a 70-kg robber 1.6 m in 0.50 s? Author: Tippens, P. (2007)

Practice Problems: 1. A 10 kg crate is being pushed to the right with a force of 500 N. It travels 3 m. What is the work done by the applied force? If there is a frictional force of 50 N, then what is the work done by the frictional force? (positive or negative?) How much work is done by gravity? What is the net work done on the crate?

Your Turn! A force of 100 N is applied to an object. It moves 5 m at a constant speed. What is the work done by the applied force? What is the work done by friction? What is the net work done on the object? How much power was used by the applied force if it moved 5 m in 3 seconds? Pause for Practice 100 N Show your work for credit Ans: 500 J; -500 J; 0 J; 166.7 W

Save for Class! 3. A force of 100 N and 200 N is applied to an block over a distance of 3 m. The block moves to the right. What is the net force? What is the acceleration? What is the net work done on the object? Which force did positive work? Which force did negative work? If the block returned to its original position, then what would be the net work done on the box? 100 N 200 N 2 kg

Bellringer Questions You have 2 minutes to answer the following questions. A force of 50N is applied to an object to move at constant speed. What is the frictional force? If the object moved 5 meters, then how much work was done by the applied force? Work is a ___quantity. A. Scalar B. Vector

Energy is the capability for doing work. Energy is anything that can be converted into work; i.e., anything that can exert a force through a distance. Energy is the capability for doing work. Author: Tippens, P. (2007)

Potential Energy Potential Energy: Ability to do work by virtue of position or condition. A suspended weight A stretched bow Author: Tippens, P. (2007)

Work and Potential Energy (Joules)                                                                                The work done on the ball gives the ball gravitational potential energy.   At this point gravity has the potential to work on the object. (fall) PEg = mgh Hewitt, P. [Illustrations]. Conceptual Physics.

Gravitational Potential Energy Work & Energy Notes Example Problem: What is the potential energy of a 50-kg person in a skyscraper if he is 480 m above the street below? Gravitational Potential Energy What is the P.E. of a 50-kg person at a height of 480 m? Author: Tippens, P. (2007)

A speeding car or a space rocket Kinetic Energy Kinetic Energy: Ability to do work by virtue of motion. (Mass with velocity) A speeding car or a space rocket Author: Tippens, P. (2007)

Examples of Kinetic Energy Work & Energy Notes Examples of Kinetic Energy What is the kinetic energy of a 5-g bullet traveling at 200 m/s? 5 g 200 m/s What is the kinetic energy of a 1000-kg car traveling at 14.1 m/s?

Total Mechanical Energy PEg + KE Determine the total mechanical energy (TME) at each point on the hills. PE = 5,000 J KE = 0 PE = 3,000 J KE = 1,500 J

Total Mechanical Energy PEg + KE Pause for Practice Total Mechanical Energy PEg + KE Determine the height and speed of the ball at each point. Mass of ball = 5 kg PE = 5,000 J KE = 0 PE = 3,000 J KE = 1,500 J

Conservation of Mechanical Energy: If only conservative forces (like gravity, not friction or air resistance) are acting , the total mechanical energy of a system neither increases nor decreases in any process. It stays constant – it is conserved. KEo + PEo = KEf + PEf or Total MEo = Total MEf = Constant Law of Conservation of Energy: The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one body to another, but the total amount remains constant. Energy in Skate Park

Energy Transformation                                                                                    Etot= mgh3             Etot = mgh2 + 1/2 mv22           Etot = 1/2 mv12            Etot = mgh3 h3 h3 h2 h = 0 Etot = Total Mechanical Energy

Conservation of Mechanical Energy: Etot = KE + PE (Neglect Air and Friction)

Energy - Sample Problems: Question: If energy is conserved, then why doesn’t the pendulum keep swinging forever, or a roller coaster continue to move forever? What is happening?

External Forces & Work The work done by an external force (air resistance, friction, external push) causes a loss or gain in mechanical energy. Example: Work done by Friction causes a loss – energy is converted to heat

Total energy is the sum of both types of energy. Energy Conservation                     Total energy is the sum of both types of energy. (Exclude air resistance) The Physics Classroom [Animation]

Pause for Practice Your Turn!

Energy - Sample Problems: (Save for Class!) Energy - Sample Problems: A 10 kg object is released 10 m above ground. a) What is the PEg, KE, and total energy of the object 10 m above the ground? b) What is the PEg after the object has fallen 2 m? c) What is the object’s KE just before striking the ground? d) What is the object’s speed just before striking the ground?

Save for Class! Use conservation of energy to determine the biker’s final speed. (Hint: Why is mass not needed?)

Bellringer Questions You have 2 minutes to answer the following questions. When reaching terminal velocity, your acceleration is 9.8 m/s2 B. 0 m/s2 C. Cannot be determined Work done by friction causes An increase in mechanical energy A decrease in mechanical energy Which of the following is an example of KE? A. Water at a dam B. A Tornado C. A Pendulum at rest

Bellringer Questions You have 2 minutes to answer the following questions. Energy of position or stored energy is called Work C. Potential Energy B. Kinetic Energy D. Power A ball is dropped from a given height. As the ball falls which of the following increases A. Kinetic energy B. Potential energy How much work is gravity doing if a 5 kg box is pushed horizontally along the floor 2m? A. 0 J B. 10 J C. 98 J

Work = F x d = Area under Force vs. Displacement graph What is the work done between 3 to 5 meters?

Work from Graph Force (N) + --

Determine the Work between positions 4.0m and 6.0m Pause for Practice Your Turn! Determine the Work between positions 4.0m and 6.0m Area = 100 J

Spring Force varies linearly with the displacement. FPull = kx Springs Spring Force varies linearly with the displacement. FPull = kx Hooke’s Law: Fs (Restoring Force) = -kx K = Spring Constant (N/m)

F xf Elastic Potential Energy

Spring Applet Spring Simulation

Sample Problem A spring with a constant of 400 N/m is compressed horizontally by 5 cm. A 500 g ball is placed against the end of the spring and then released. What is the Potential Energy of the spring? What will be the velocity of the ball when it passes through the equilibrium position?

Your Turn! Ans: 200 N/m Ans: 1.58 m/s Pause for Practice 1. A force of 10 N is used to compress a spring horizontally by 5 cm. a) What is the spring constant? Pause for Practice Ans: 200 N/m b) If a 200 g object is placed on the spring, what will be the object’s velocity when released at the equilibrium position? (Think Conservation of Energy!) Ans: 1.58 m/s

Change in KE is work. The Physics Classroom [Illustration]

Work and Kinetic Energy A resultant force changes the velocity of an object and does work on that object. m vo vf d F Author: Tippens, P. (2007)

The Work-Energy Theorem Work is equal to the change in ½mv2 If we define kinetic energy as ½mv2 then we can state a very important physical principle: The Work-Energy Theorem: The work done by a resultant force is equal to the change in kinetic energy that it produces. Author: Tippens, P. (2007)

Practice Problems A 4 kg block starts from rest and reaches a speed of 5 m/s over a distance of 5 m. What is the change in KE? What is the work done on the block? How much force was applied to the block?

Ans: 10 m/s (both B and C) Pause for Practice Your Turn! (Think Conservation of Energy) If the object begins with an initial speed of 2 m/s, then what is its speed at point B? point C? Why is mass not given? Ans: 10 m/s (both B and C)

Credits: Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons. Foxtrot Cartoon: Bill Amend. Received from 2007 AP Conference Complimentary Resource CD. Hewitt, P. [Illustrations]. Conceptual Physics. Nave, R. (2010). Hyperphysics.[Illustration]. Permission granted to use illustrations. Retrieved from http://hyperphysics.phyastr.gsu.edu/hbase/hframe.html Tippens, P. (2007). Chapter 8A Work [PowerPoint Slides]. Received from 2007 AP Conference Complimentary Resource CD. Tippens, P. (2007). Chapter 8B Work and Energy [PowerPoint Slides]. Received from 2007 AP Conference Complimentary Resource CD. The Physics Classroom]. http://www.thephysicsclassroom.com