Work, Energy and Power!

1. 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 position • Kinetic energy : is the energy of motion • Potential Energy : an object can store energy as the result of its position or elastic source

4. Work • In physics, work has a very specific meaning. • 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 displacement • Mathematically, work can be expressed by the following equation. • W= F x d cos q ( cos 00 = 1) • where 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) Force (N) W = F x d Work (joules) Distance (m)

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

8. Work Calculations W=F x d W=F x d cos 300 W= F x d =100N X 5m = 100N X 5m X .87 =15Kg(10m/s2) 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. • 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 m • PE = mgh • PE = (5Kg)(10 m/s2)(4.5 m) • PE = 225 Kg m2/s2 • PE = 225 J

11. Kinetic Energy Calculation • The energy of motion • DKE = W= F x d= mgh=1/2 mv2 • Find the kinetic energy of an 4 Kg object moving at 5m/s. • KE = 1/2 mv2 • KE = ½ (4Kg)(5m/s) 2 • KE = 50 Kg m 2 /s 2 • KE = 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 m • W = .5 J (each push up) • 10 pushups = 5 J • PE = ½ k x 2 • .5 J = ½ k (.05m) 2 • .5 J = ½ k (.003m 2) • .5 J = .0015 m 2 • 333.3 J/m 2 = k

15. Power! • Power is the rate that we use energy. • Power = Work or Energy / Time • P = W/t = F x d/t = F v • The units for power : • J/s • Kg m2 / s2 /s • N m / s

16. 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 109 W) of power!

17. More Power Examples • Hydroelectric plant • Drops water 20 m, with flow rate of 2,000 m3/s • 1 m3 of water is 1,000 kg, or 9,800 N of weight (force) • Every 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 m2 Fdrag1800 N • In each second, car goes 30 m  W = 180030 = 54 kJ • So power = work per second is 54 kW (72 horsepower) • Bicycling up 10% (~6º) slope at 5 m/s (11 m.p.h.) • raise your 80 kg self+bike 0.5 m every second • mgh = 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. • P = F x d / t • P = 30 N (10 m) / 5 s • P = 60 N m /s • P = 60 watts

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