1. Work, Energy and Power! Work, Energy and Power! The Calculations and Equations

2. Energy and Work Energy is the ability to do work. Work is the energy transferred to or from a system by a force that acts on it.

3. Mechanical Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of positionMechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position Kinetic energy : is the energy of motion Kinetic energy : is the energy of motion Potential Energy : an object can store energy as the result of its position or elastic source Potential Energy : an object can store energy as the result of its position or elastic source

4. Work Work In physics, work has a very specific meaning.In physics, work has a very specific meaning. In physics, work represents a measurable change in a system, caused by a force.In physics, work represents a measurable change in a system, caused by a force.

5. Work Concept Work is defined as a force acting upon an object to cause a displacementWork is defined as a force acting upon an object to cause a displacement Mathematically, work can be expressed by the following equation.Mathematically, work can be expressed by the following equation. W= F x d cos  cos 0 0 = 1) W= F x d cos  cos 0 0 = 1) where F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vectorwhere F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vector

6. Work (force is parallel to distance) W = F x d Distance (m) Force (N) Work (joules)

7. Work (force at angle to distance) W = Fd cos ( q ) Distance (m) Force (N) Work (joules) Angle

8. Work Calculations W=F x dW=F x d cos 30 0 W= F x d =100N X 5m = 100N X 5m X.87 =15Kg(10m/s 2) X 5m =500 N m = 413 N m = 750 N m

9. Gravitational Potential Energy After an object has been lifted to a height, work is done.After an object has been lifted to a height, work is done. PE = W= F x d= mgh PE = W= F x d= mgh Potential Energy is maximum at the maximum HEIGHT

10. Potential Energy Calculation How much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 mHow much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 m PE = mghPE = mgh PE = (5Kg)(10 m/s 2 )(4.5 m)PE = (5Kg)(10 m/s 2 )(4.5 m) PE = 225 Kg m 2 /s 2PE = 225 Kg m 2 /s 2 PE = 225 JPE = 225 J

11. Kinetic Energy Calculation The energy of motionThe energy of motion  KE = W= F x d= mgh=1/2 mv 2 Find the kinetic energy of an 4 Kg object moving at 5m/s.Find the kinetic energy of an 4 Kg object moving at 5m/s. KE = 1/2 mv 2KE = 1/2 mv 2 KE = ½ (4Kg)(5m/s) 2KE = ½ (4Kg)(5m/s) 2 KE = 50 Kg m 2 /s 2KE = 50 Kg m 2 /s 2 KE = 50 JKE = 50 J

12. Elastic potential energy

13. Spring constant Calculation A tired squirrel (mass of 1 kg) does push- ups by applying a force to elevate its center-of-mass by 5 cm. (A) Determine the number of push-ups which a tired squirrel must do in order to do a mere 5.0 Joules of work. (B) Determine the squirrel’s spring constant.

14. Spring Constant Calculation W = F x d = 10 N*(.05m)=.5 N mW = F x d = 10 N*(.05m)=.5 N m W =.5 J (each push up) W =.5 J (each push up) 10 pushups = 5 J 10 pushups = 5 J PE = ½ k x 2 PE = ½ k x 2.5 J = ½ k (.05m) 2.5 J = ½ k (.05m) 2.5 J = ½ k (.003m 2 ).5 J = ½ k (.003m 2 ).5 J =.0015 m 2.5 J =.0015 m 2 333.3 J/m 2 = k333.3 J/m 2 = k

15. Power! Power is the rate that we use energy.Power is the rate that we use energy. Power = Work or Energy / TimePower = Work or Energy / Time P = W/t = F x d/t = F vP = W/t = F x d/t = F v The units for power :The units for power : J/sJ/s Kg m 2 / s 2 /sKg m 2 / s 2 /s N m / sN m / s

16. Spring 200816 Power Power is simply energy exchanged per unit time, or how fast you get work done (Watts = Joules/sec) One horsepower = 745 W Perform 100 J of work in 1 s, and call it 100 W Run upstairs, raising your 70 kg (700 N) mass 3 m (2,100 J) in 3 seconds  700 W output! Shuttle puts out a few GW (gigawatts, or 10 9 W) of power!

17. Spring 200817 More Power Examples Hydroelectric plantHydroelectric plant Drops water 20 m, with flow rate of 2,000 m 3 /sDrops water 20 m, with flow rate of 2,000 m 3 /s 1 m 3 of water is 1,000 kg, or 9,800 N of weight (force)1 m 3 of water is 1,000 kg, or 9,800 N of weight (force) Every second, drop 19,600,000 N down 20 m, givingEvery second, drop 19,600,000 N down 20 m, giving 392,000,000 J/s  400 MW of power Car on freeway: 30 m/s, A = 3 m 2  F drag  1800 NCar on freeway: 30 m/s, A = 3 m 2  F drag  1800 N In each second, car goes 30 m  W = 1800  30 = 54 kJIn each second, car goes 30 m  W = 1800  30 = 54 kJ So power = work per second is 54 kW (72 horsepower)So power = work per second is 54 kW (72 horsepower) Bicycling up 10% (~6º) slope at 5 m/s (11 m.p.h.)Bicycling up 10% (~6º) slope at 5 m/s (11 m.p.h.) raise your 80 kg self+bike 0.5 m every secondraise your 80 kg self+bike 0.5 m every second mgh = 80  9.8  0.5  400 J  400 W expendedmgh = 80  9.8  0.5  400 J  400 W expended

18. Power Calculation A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart.A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart. P = F x d / tP = F x d / t P = 30 N (10 m) / 5 sP = 30 N (10 m) / 5 s P = 60 N m /sP = 60 N m /s P = 60 wattsP = 60 watts

19. Summary Energy is the ability to moveEnergy is the ability to move Potential is stored energy (Statics)Potential is stored energy (Statics) Dependant on heightDependant on height Kinetic is moving energy (Dynamics)Kinetic is moving energy (Dynamics) Dependant on velocityDependant on velocity Springs store energy dependant on distance and constantSprings store energy dependant on distance and constant Power is how fast the work is donePower is how fast the work is done