Chapter 7 Work and Energy

Conservation Laws Mass Mass Electric Charge Electric Charge Conservation of Energy Conservation of Energy Sum of all forms of energy is conserved Sum of all forms of energy is conserved Energy: ability to do work

Forms of Energy Mechanical Mechanical Focus for nowFocus for now May be kinetic (associated with motion) or potential (associated with position)May be kinetic (associated with motion) or potential (associated with position) Chemical Chemical Electromagnetic Electromagnetic Nuclear Nuclear

Some Energy Considerations Energy can be transformed from one form to another Energy can be transformed from one form to another Essential to the study of physics, chemistry, biology, geology, astronomyEssential to the study of physics, chemistry, biology, geology, astronomy From one body to another – Work! From one body to another – Work! Can be used in place of Newton’s laws to solve certain problems more simply Can be used in place of Newton’s laws to solve certain problems more simply

Work Provides a link between force and energy 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. 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.

Units of Work SI SI Newton meter = JouleNewton meter = Joule N m = J N m = J J = kg m 2 / s 2 J = kg m 2 / s 2 US Customary US Customary foot poundfoot pound ft lb ft lb no special nameno special name

Work, cont. In general In general F is the magnitude of the forceF is the magnitude of the force s is the distance of the object moveds is the distance of the object moved  is the angle between force and direction of motion is the angle between force and direction of motion

Work, cont. This gives no information about This gives no information about the time it took for the motion to occurthe time it took for the motion to occur the velocity or acceleration of the objectthe velocity or acceleration of the object Work is a scalar quantity Work is a scalar quantity

More About Work The work done by a force is zero when the force is perpendicular to the displacement The work done by a force is zero when the force is perpendicular to the displacement F=0F=0 s=0s=0 cos 90° = 0cos 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 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 Work can be positive or negative Positive if s is in the same direction as FPositive if s is in the same direction as F Negative if s is in opposite direction to FNegative if s is in opposite direction to F Zero if s is perpendicular to FZero if s is perpendicular to F

Work Can Be Positive or Negative Work is positive when lifting the box Work is positive when lifting the box Work would be negative if lowering the box Work would be negative if lowering the box The force would still be upward, but the displacement would be downwardThe force would still be upward, but the displacement would be downward

Example 50N force pulls a 20 kg object at 30° above horizontal and moves it 2m, friction f=15N. Acceleration along the ground? Work done? Work done by friction?

Kinetic Energy Energy associated with the motion of an object Energy associated with the motion of an object Scalar quantity with the same units as work Scalar quantity with the same units as work Work is related to kinetic energy Work is related to kinetic energy

Work-Kinetic Energy Theorem When work is done by the resultant external 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 When work is done by the resultant external 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 Speed will increase if work is positiveSpeed will increase if work is positive Speed will decrease if work is negativeSpeed will decrease if work is negative

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 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 nailThe moving hammer has kinetic energy and can do work on the nail

Example 50N force pulls a 20 kg object at 30° above horizontal and moves it 2m, friction f=15N. Find v f if v i= 4m/s.

Power Often also interested in the rate at which the energy transfer takes place Often also interested in the rate at which the energy transfer takes place Power is defined as this rate of energy transfer Power is defined as this rate of energy transfer SI units are Watts (W) SI units are Watts (W)

Power, cont. US Customary units are generally hp US Customary units are generally hp Need a conversion factorNeed a conversion factor Can define units of work or energy in terms of units of power: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 kilowatt hours (kWh) are often used in electric bills 1kWh=3.6x10^6 J This is a unit of energy, not power This is a unit of energy, not power

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?

Potential Energy Potential energy is associated with the shape or position of the object Potential energy is associated with the shape or position of the object Potential energy is a property of the system, not the objectPotential 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 systemA system is a collection of objects interacting via forces or processes that are internal to the system

Elastic Potential Energy Compression of a spring Compression of a spring Restoring force Restoring force Elastic potential energy Elastic potential energy Energy is available to do work: Energy is available to do work:

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 (PE) 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 (PE) Falling object: PE is changed to KEFalling object: PE is changed to KE PE of water in reservoir is used to generate electricityPE of water in reservoir is used to generate electricity

Example A 1500kg pile driver lifted 20 m in the air have PE …

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 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 processTo 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 In Conservation of Energy, the total mechanical energy remains constant

Conservation of Energy, cont. Total mechanical energy is the sum of the kinetic and potential energies in the system Total mechanical energy is the sum of the kinetic and potential energies in the system Other types of potential energy functions can be added to modify this equationOther types of potential energy functions can be added to modify this equation

Work and Energy If a force (other than gravity) acts on the system and does work If a force (other than gravity) acts on the system and does work Need Work-Energy relation Need Work-Energy relation or or

Example Cart on a roller-coaster…

Example Two cars each with mass 2000kg and speed 80km/h collide.

Example Child on a slide If a child of 25kg slides down and reaches only 3m/s. What work was done by the frictional force acting on the child?