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Chapter 5 Work and Energy Work and Energy • Work – describes something done to an object or system. – scientifically, is a net force applied to or by an object through a distance – W = FdII – is energy transfer. – System: box in a warehouse – Environment: you, gravitational field, and anything external to the box • Work Work and Energy – is positive when energy is transferred to the system. – is negative when energy is transferred out of the system – occurs only when the displacement is in the direction parallel to the force – is measured in joules (J) – 1 J = 1 N.m = 1 kg.m2/s2 NO WORK! Work and Energy • Work W = F cosq d or W = Fd cosq This is the definition of work. The magnitude of the force vector times the magnitude of the displacement vector times the cosine of the angle between the vectors. Work and Energy • Work moving from A to B W = Fgd moving from B to C W = - Fgd Total work = 0 Fapp Fapp Fapp d A B C Work and Energy • Energy – is a conserved quantity with the capability to produce change in itself and its environment. – is the property of a system that describes its ability to produce change. – is measured in joules – 1J = 1 kg.m2/s2 – Thermal – Chemical – Energy of motion Work and Energy • Kinetic Energy – associated with motion – KE = ½mv2 – the work an object can do while changing speed – the amount of energy in a moving object Work and Energy Suppose that an automobile of mass m is traveling with velocity vi when the motor is shut off and the brakes are applied (locked). If the friction force between the pavement and the squealing tires is Ff, how much work does the car do against this force by the time it comes to rest? W = Fd vf2 = vi2 - 2ad assuming constant acceleration 2ad = vf2 - vi2 and ad = 1/2 (vf2 - vi2 ) Using Newton’s 2nd law: a= F m F d = ad = 1/2 (v 2 - v 2 ) f i m Fd = 1/2 m(vf2 - vi2 ) Work done = 1/2 m(vf2 - vi2 ) Work and Energy • Energy – Work done = 1/2 m(vf2 - vi2 ) = 1/2 mvf2 - 1/2 mvi2 – The ability of a moving object to do work because of its motion forms the basis for the definition of the quantity kinetic energy (KE). – Work done is equal to the change in kinetic energy is true even if the acceleration is not uniform. – Work done is the same thing as net work or Wnet. Work and Energy • Work - Kinetic Energy Theorem Wnet = DKE F.d.cosq = ½mvf2 – ½ mvi2 The net work done by a net force acting on an object is equal to the change in the kinetic energy of the object. + Wnet then speed increases Chapter 5 Section 2 Energy Sample Problem Work-Kinetic Energy Theorem On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 1. Define Given: m = 10.0 kg vi = 2.2 m/s vf = 0 m/s µk = 0.10 Unknown: d=? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued Work-Kinetic Energy Theorem 2. Plan Choose an equation or situation: This problem can be solved using the definition of work and the work-kinetic energy theorem. Wnet = Fnetdcosq The net work done on the sled is provided by the force of kinetic friction. Wnet = Fkdcosq = µkmgdcosq Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued DKE = Wnet 3. Calculate ½mvf2 – ½ mvi2 = F.d.cosq 0 – ½ mvi2 = m . mg.d.cosq (–2.2 m/s)2 d 2(0.10)(9.81 m/s2 )(cos180) d 2.5 m Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Work and Energy • Conservation of Energy Conserved means remains constant. Total energy is conserved. Energy can be converted from one form to another but the total amount of energy remains constant! What is another quantity that is conserved? Work and Energy ENERGY Mechanical Kinetic Nonmechanical Potential Gravitational Elastic Work and Energy • Potential Energy – the amount of work an object is capable of doing because of its position • Gravitational potential energy is the potential energy stored in the gravitational fields of interacting bodies. • Gravitational potential energy depends on height from a designated zero or reference level. PEg = mgh gravitational PE = mass free-fall acceleration height Work and Energy • Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration. PEelastic elastic PE = 1 1 2 kx 2 spring constant (distance compressed or stretched) 2 • The symbol k is called the spring constant, a parameter that measures the spring’s resistance to being compressed or stretched. 2 Chapter 5 Section 2 Energy Elastic Potential Energy Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem Potential Energy A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 1. Define Given:m = 70.0 kg k = 71.8 N/m g = 9.81 m/s2 h = 50.0 m – 44.0 m = 6.0 m x = 44.0 m – 15.0 m = 29.0 m PE = 0 J at river level Unknown: PEtot = ? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 2. Plan Choose an equation or situation: The zero level for gravitational potential energy is chosen to be at the surface of the water. The total potential energy is the sum of the gravitational and elastic potential energy. PEtot PEg PEelastic PEg mgh PEelastic 1 2 kx 2 Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 3. Calculate Substitute the values into the equations and solve: PEg (70.0 kg)(9.81 m/s2 )(6.0 m) = 4.1 10 3 J 1 PEelastic (71.8 N/m)(29.0 m)2 3.02 10 4 J 2 PEtot 4.1 103 J + 3.02 10 4 J PEtot 3.43 10 4 J Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 5 Section 2 Energy Sample Problem, continued Potential Energy 4. Evaluate One way to evaluate the answer is to make an order-of-magnitude estimate. The gravitational potential energy is on the order of 102 kg 10 m/s2 10 m = 104 J. The elastic potential energy is on the order of 1 102 N/m 102 m2 = 104 J. Thus, the total potential energy should be on the order of 2 104 J. This number is close to the actual answer. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Work and Energy • Mechanical Energy: the sum of kinetic energy and all forms of potential energy ME = KE + SPE • Conservation of Mechanical Energy – In the absence of friction mechanical energy is conserved. • MEi = MEf • KEi + PEi = KEf + PEf • Energy conservation occurs even when acceleration varies and the kinematic equations are not valid. Work and Energy • Mechanical Energy: is the ability to do work • Conservation of Mechanical Energy ME = KE + SPE – In the absence of friction mechanical energy is conserved. • MEi = MEf • KEi + PEi = KEf + PEf • Why is mechanical energy not conserved in the presence of friction? Work and Energy • Power – is the rate at which work is done. – is the rate of energy transfer. P = W/t = work / time P = Fd/t P = Fv – J/s = Watt (W) – Horsepower (hp) = 746 W