Chapter 5 Energy 5 1 Work Work F Dx 5 1 Work The work W done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement This gives no information about the time it took for the displacement to occur the velocity or acceleration of the object Work is a scalar quantity Page 1 Work W F cos q Dx F is the magnitude of the force x is the magnitude of the object s displacement q is the angle between F and Dx Work done example The total mass of fish and sled 50 kg F 120 N and he pulls it for 5 m How much work is done if q 0 How much work is done if q 30o Page 2 Work W F cos q Dx F is the magnitude of the force x is the magnitude of the object s displacement q is the angle between When Work is Zero Displacement is horizontal Force is vertical cos 90 0 Page 3 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 5 2 Kinetic Energy Energy associated with the motion of an object KE 1 mv 2 2 Scalar quantity with the same units as work Work is related to kinetic energy Page 4 5 2 The Work Energy Theorem and Kinetic Energy Energy when work is done energy changes Many forms of energy chemical energy nuclear energy electric magnetic energy mechanical energy Total energy is conserved Energy can do things Work Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed the work done is equal to the change in the object s kinetic energy Wnet KEf KEi DKE Speed will increase if work is positive Speed will decrease if work is negative Page 5 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 Types of Forces There are two general kinds of forces Conservative Work and energy associated with the force can be recovered Nonconservative The forces are generally dissipative and work done against it cannot easily be recovered Page 6 Any force that is conservative can be represented by an energy easy to calculate Gravity gravitational potential energy Spring force spring energy If the work done by the force depends on the path it is nonconservative Can t name an energy after it and it has to be calculated case by case or more accurately path by path Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points The work depends only upon the initial and final positions of the object Any conservative force can have a potential energy function associated with it Page 7 More About Conservative Forces Examples of conservative forces include Gravity Spring force Electromagnetic forces Potential energy is another way of looking at the work done by conservative forces Nonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points Examples of nonconservative forces kinetic friction air drag propulsive forces Page 8 Friction as a Nonconservative Force The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature The objects are warmer than they were before the movement Internal Energy is the term used for the energy associated with an object s temperature Friction Depends on the Path The blue path is shorter than the red path The work required is less on the blue path than on the red path Friction depends on the path and so is a non conservative force Page 9 5 3 Gravitational Potential Energy Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth s surface Objects interact with the earth through the gravitational force Work and Gravitational Potential Energy PE mgy Wgrav ity PEi PEf Units of Potential Energy are the same as those of Work and Kinetic Energy Page 10 5 4 Potential Energy Stored in a Spring Involves the spring constant k Hooke s Law gives the force F kx F is the restoring force F is in the opposite direction of x k depends on how the spring was formed the material it is made from thickness of the wire etc Potential Energy in a Spring Elastic Potential Energy related to the work required to compress a spring from its equilibrium position to some final arbitrary position x 1 PEs 2 kx 2 Page 11 Conservation of Energy Including a Spring The PE of the spring is added to both sides of the conservation of energy equation KE PEg PEs i KE PEg PEs f The same problem solving strategies apply Nonconservative Forces with Energy Considerations When nonconservative forces are present the total mechanical energy of the system is not constant The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system Wnc DEnergy Page 12 Notes About Conservation of Energy We can neither create nor destroy energy Another way of saying energy is conserved If the total energy of the system does not remain constant the energy must have crossed the boundary by some mechanism Applies to areas other than physics Transferring Energy By Work By applying a force Produces a displacement of the system Page 13 Transferring Energy Heat The process of transferring heat by collisions between molecules For example the spoon becomes hot because some of the KE of the molecules in the coffee is transferred to the molecules of the spoon as internal energy Transferring Energy Electrical transmission Transfer by means of electrical current This is how energy enters any electrical device Page 14 Power Often also interested in the rate at which the energy transfer takes place Power is defined as this rate of energy transfer W Fv t SI units are Watts W W J kg m2 s s2 Page 15