Chapter 5 Work, Power and Energy Work Provides a link between force and energy The work, W, done by a constant force on an object is the product of the force times the distance through which the force acts. W Fs Units of Work SI • Newton • meter = Joule N•m=J J = kg • m2 / s2 US Customary • foot • pound ft • lb • no special name Work, cont. In general W ( F cos ) s • F is the magnitude of the force • s (or d) is the distance of the object moved • is the angle between force and direction of motion Work, cont. This gives no information about • the time it took for the motion to occur • the velocity or acceleration of the object Work is a scalar quantity More About Work The work done by a force is zero when the force is perpendicular to the displacement • F=0 • s=0 • cos 90° = 0 If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force More About Work, cont. Work can be positive or negative • Positive if s is in the same direction as F • Negative if s is in opposite direction to F • Zero if s is perpendicular to F Work Can Be Positive or Negative Work is positive when lifting the box Work would be negative if lowering the box • The force would still be upward, but the displacement would be downward Example 50N force pulls a 20 kg object and moves it 2m, friction f=15N. Acceleration along the ground? Work done? Work done by friction? Total work? What about pulling at 30? Power Power is defined as this rate of work • W P t SI units are Watts (W) • J kg m 2 W 3 s s Power, cont. US Customary units are generally hp • Need a conversion factor ft lb 1 hp 550 746 W s • Can define units of work or energy in terms of units of power: kilowatt hours (kWh) are often used in electric bills 1kWh=3.6x10^6 J This is a unit of energy, not power Example A crane lifts a 5000 kg object 800 m in 10 min. How much power must the engine produce? Example An 80hp outboard motor, operating at full speed, can drive at speed boat at 11 m/s. What is the forward thrust(force) of the motor? W Fs P Fv t t Conservation Laws Mass Electric Charge Conservation of Energy Sum of all forms of energy is conserved Energy: ability to do work Forms of Energy Mechanical • Focus for now • May be kinetic (associated with motion) or potential (associated with position) Chemical Electromagnetic Nuclear Some Energy Considerations Energy can be transformed from one form to another • Essential to the study of physics, chemistry, biology, geology, astronomy From one body to another – Work! Can be used in place of Newton’s laws to solve certain problems more simply Potential Energy Potential energy is associated with the shape or position of the object • Potential energy is a property of the system, not the object • A system is a collection of objects interacting via forces or processes that are internal to the system Gravitational Potential Energy Lift object vertically, work is done against the force of gravity of Earth and energy is stored in the object in the form of Gravitational Potential Energy (Ep) • PE of water in reservoir is used to generate electricity E p mgh Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen for each problem • The choice is arbitrary since the change in the potential energy is the important quantity • Choose a convenient location for the zero reference height often the Earth’s surface may be some other point suggested by the problem • Once the position is chosen, it must remain fixed for the entire problem Example A 1500kg pile driver lifted 20 m in the air have EP … Kinetic Energy Energy associated with the motion of an object 1 2 Ek mv 2 Scalar quantity with the same units as work Work is related to kinetic energy Work and Kinetic Energy An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest • The moving hammer has kinetic energy and can do work on the nail Example Consider energy of a falling ball of mass m from height of h. Energy Conservation Energy is never created or destroyed. Energy can be transformed from one kind into another, but the total amount of energy remains constant. Example: Pendulum Conservation of Mechanical Energy Conservation in general • To say a physical quantity is conserved is to say that the numerical value of the quantity remains constant throughout any physical process In Conservation of Energy, the total mechanical energy remains constant E E p Ek constant Conservation of Energy, cont. Total mechanical energy is the sum of the kinetic and potential energies in the system Ei E f E pi Eki E pf Ekf • Other types of potential energy functions can be added to modify this equation Conservation of (mechanical) Energy True if only conservative forces are present • Conservative forces: gravity, springs • Non-conservative forces: push, pull, friction, air-resistance Apply the conservation of energy equation to the system • Immediately substitute zero values, then do the algebra before substituting the other values Solve for the unknown(s) Work and Energy If a force (other than gravity) acts on the system and does work Need Work-Energy relation E pi Eki Wnc E pf Ekf Wnc work done by non-cons. forces 1 2 1 2 mghi mvi W mghf mv f 2 2 Example Cart on a roller-coaster with no friction. Start from rest at h=30m. What is the speed at the end hA=15m. Example Two cars each with mass 2000kg and speed 80km/h collide and come to rest. Example Child on a 3 m high slide (no friction), what is the speed at the end? If a child of 25kg slides down from rest and reaches only 3m/s. What work was done by the frictional force acting on the child? If the slide is 10 m long, how large was the average friction force? Example Same child is on a swing with 6m rope and starts at 60° with respect to vertical direction. Maximum speed? If the child starts with speed of 1 m/s with a push, what is the max speed?