Work Energy and Power The Calculations and Equations

Work, Energy and Power! The Calculations and Equations

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.

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

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

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

Work (force is parallel to distance) Force (N) Work (joules) W=Fxd Distance (m)

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

Work Calculations W=F x d cos 300 =100 N X 5 m =500 N m = 100 N X 5 m X. 87 = 413 N m W= F x d =15 Kg(10 m/s 2) X 5 m = 750 N m

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

Potential Energy Calculation • How much potential energy is lost by a 5 Kg object to kinetic energy due a decrease in height of 4. 5 m • PE = mgh • PE = (5 Kg)(10 m/s 2)(4. 5 m) • PE = 225 Kg m 2/s 2 • PE = 225 J

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

Elastic potential energy

Spring constant Calculation A tired squirrel (mass of 1 kg) does pushups 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.

Spring Constant Calculation • • W = F x d = 10 N*(. 05 m)=. 5 N m W =. 5 J (each push up) 10 pushups = 5 J PE = ½ k x 2. 5 J = ½ k (. 05 m) 2. 5 J = ½ k (. 003 m 2). 5 J =. 0015 m 2 333. 3 J/m 2 = k

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 m 2 / s 2 /s • Nm/s

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! Spring 2008 16

More Power Examples • Hydroelectric plant • • • Drops 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) Every second, drop 19, 600, 000 N down 20 m, giving 392, 000 J/s 400 MW of power • Car on freeway: 30 m/s, A = 3 m 2 Fdrag 1800 N • In each second, car goes 30 m W = 1800 30 = 54 k. J • So power = work per second is 54 k. W (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 Spring 2008 17

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

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