Work Power Energy

Work Concepts Work (W) ~ product of the force exerted on an object and distance the object moves in the direction of the force. Work (W) ~ product of the force exerted on an object and distance the object moves in the direction of the force. W is transfer of energy by mechanical means. W is transfer of energy by mechanical means. W is done on an object only if it moves in the direction of the force. W is done on an object only if it moves in the direction of the force. Only the component of the force in the direction of the motion does work. Only the component of the force in the direction of the motion does work.

Work Equations W net = F net x displacement x (cos  ) W net = F net d (cos  Note: F = m x a so W = m x a x d Or: work makes you “mad” Unit: work = newton * meter or Nm This is also known as a “joule” or j which is commonly used for energy Here, the horizontal component provides the forward force F x = FcosӨ F x = FcosӨ Here, the force is parallel to the motion so cos 0 o = 1 F d F  d

The Sign of Work Positive work is done when the motion is in the same direction as the force of motion. For a moving object Positive work is done when the motion is in the same direction as the force of motion. For a moving object (+) net work results in increased velocity. Negative work results from a force applied in the direction opposite the motion. For a moving object Negative work results from a force applied in the direction opposite the motion. For a moving object (-) net work results in decreased velocity. F f d F does (+) work f does (-) work

Energy Energy (the ability to do work) MechanicalNon-mechanical MechanicalNon-mechanicalchemical Kinetic Potential thermal Kinetic Potential thermal K = ½ mv 2 nuclear Gravitational Elastic U g = mgh U s = ½ kx 2 U g = mgh U s = ½ kx 2

Mechanical Energy Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position, shape, or form E total = K total + U total

Kinetic Energy K = ½ x mass x velocity² Kinetic energy is the energy an object has because of its motion

Work-Energy Theorem According to the Work-Energy theorem, the work done on an object, by the net force acting on it, is equal to the change in kinetic energy of the body Work =  K F d cos  = K f - K i

Potential Energy Potential energy (U) is the energy an object has because of its position, shape, or form There are two types of PE: gravitational spring (or elastic)

Gravitational P E U g = mgh (mass x gravity x height) Gravitational potential energy depends on the weight of the body and its position in a gravity field Where is Ug measured from? If A is your reference point then points B and C have –U. If C is your reference, then B and A have +U.

Elastic PE U s = ½ kx 2 Elastic potential energy is energy stored within an elastic system. This energy is based on two factors: Elastic potential energy is energy stored within an elastic system. This energy is based on two factors: The constant, k, (called the spring constant) is based on the type of material and twist of the spring The constant, k, (called the spring constant) is based on the type of material and twist of the spring The distance, x, the spring is stretched or compressed from its rest position The distance, x, the spring is stretched or compressed from its rest position

Conservation of Energy According to the law of conservation of energy, the total energy of a closed, isolated system is constant K i + U g i + U s i = K f + U g f + U s f E initial = E final

Power Power (P) ~ rate at which work is done or rate at which energy is transferred. Measured in watts. Power (P) ~ rate at which work is done or rate at which energy is transferred. Measured in watts. Power = Work / time Power = Work / time 1 watt = 1 joule / second (J/s Watt (W) ~ one joule of energy transferred in one second. Watt (W) ~ one joule of energy transferred in one second. Alternate: P = F x (d / t) so P = F x v Alternate: P = F x (d / t) so P = F x v

Simple Machines A simple machine is one in which the work (or transfer of energy) is done by one motion. A simple machine is one in which the work (or transfer of energy) is done by one motion. Work is done ON the machine to operate it – this is considered “work in ” Work is done ON the machine to operate it – this is considered “work in ” so that the machine can do work ON the object or load – this is considered “work out ” so that the machine can do work ON the object or load – this is considered “work out ”

Ideal Machines In the real world, energy is lost to friction In the real world, energy is lost to friction So, W in = W out + W f So, W in = W out + W f Ideal machines exist only in a frictionless, air resistance-less world. Ideal machines exist only in a frictionless, air resistance-less world. No energy or work is lost to the system through outside forces No energy or work is lost to the system through outside forces For ideal machines (W f = 0) : Work input = Work output F in d in = F out d out For ideal machines (W f = 0) : Work input = Work output F in d in = F out d out Note: energy always conserved Note: energy always conserved

Mechanical Advantage How much the machine multiplies the effort How much the machine multiplies the effort IMA (ideal MA) : ratio of the dimensions of the machine IMA (ideal MA) : ratio of the dimensions of the machine IMA = d in / d out IMA = d in / d out AMA (actual MA) : ratio of the actual force output (load) to force input AMA (actual MA) : ratio of the actual force output (load) to force input AMA = F out / F in AMA = F out / F in

Efficiency Efficiency : ratio of work output to work Efficiency : ratio of work output to work input expressed in percent. input expressed in percent. Also: Ratio of mechanical advantage Also: Ratio of mechanical advantage efficiency = (W out / W in ) x 100 Or efficiency = (AMA /IMA) x 100