Energy, Work and Power

Work, Energy and Power Objectives: Describe the relationship between work and energy Calculate the work done by a constant applied force Calculate the power used

Work What is work? Work transfers energy between objects W = F d W = work F = constant force d = displacement (distance moved) Unit of work = Joule (J) Joule (J) = Nm = kgm 2 /s 2

Work

Force applied at an angle: Keep in mind: Work is only done by the force in the direction of motion W = F d cos θ

Potential Energy (U) What is potential energy (U)? Potential energy - Energy of position or location, “stored” energy Gravitational potential energy (U g ) = m g h m = mass g = acceleration of gravity m/s 2 h = height (relative) Unit = Joule = kgm 2 /s 2

Kinetic Energy (K) What is kinetic energy (K)? Kinetic energy - Energy of motion Objects in motion have the ability to do work K = ½ m v 2 Unit = Joule = kgm 2 /s 2

Work-Energy Theorem Work-Energy Theorem – when work is done on an object, the result is a change in kinetic energy; or Work equals the change in kinetic energy W = ΔK Work is a transfer of energy by mechanical means.

Kinetic Energy (K) Practice: A rifle can shoot a 4.20 g bullet at a speed of 965 m/s What is the kinetic energy of the bullet as it leaves the rifle? K = ½ m v 2 = ½ kg x = 1956 J What work is done on the bullet from rest to it leaving the muzzle? Work is a transfer of energy. K is energy and we go from 0 J to J, thus ΔK = W; so Work = 1,956 J What is the average force applied to the bullet if the muzzle is 0.75 m? W = F d; so F = W/d = 1, J / 0.75 m F = 2,607 N

Power What is power? Power – Rate that work is done, or the rate that energy is transferred P = W / t Unit of Power = J/s = Watt

Power Practice: An electric motor lifts an elevator 9.00 m in 15.0 s by exerting an upward force of 1.20 x 10 4 N. What power does the motor produce in watts and kilowatts? Work = F d = 1.20 x 10 4 N x 9.00 m = 108,000 J Power = W / t = 108,000 J / 15 s P = 7200 W; 7.20 kW

Inquiring minds want to know… Work - transfers energy between objects W = F d Potential energy - Energy of position or location, “stored” energy U g = m g h Kinetic energy - Energy of motion KE = ½ m v 2 Work-Energy Theorem W = KE;, or F d = ½ m v 2 Power – Rate that work is done, or the rate that energy is transferred P = W / t A weightlifter lifts a 1 kg barbell 2 m over their head at a constant velocity. What is the Work, PE and KE when the barbell is at rest on the mat? What is the Work done on the barbell when it is lifted above the weightlifter’s head? What is the KE required to raise the barbell over the weightlifter’s head? What Work is being done on the barbell when the weightlifter holds the barbell over their head? What is the KE and PE of the barbell when it is held 2 m over the weightlifter’s head?

Inquiring minds want to know… If you draw the string back on a bow with an arrow, are you doing work? Yes, you are applying a force over a distance. What kind of energy does the bow string have when fully drawn? Potential energy (PE) (note, this PE is not dependent on gravity) What kind of energy does the arrow have after the string is released? Kinetic energy (KE)

Law of Conservation of Energy Law of Conservation of Energy – Energy cannot be created or destroyed; only transformed from one form into another. Note: 100% PE = KE + PE = 100% KE

Machines Machine – A device used to multiply forces, change the direction of forces or increase distance. Keep in mind: a machine can multiply forces, but not work or energy. Conservation of Energy – work input = work output, thus F d = F d Mechanical advantage (MA) = output F / input F, or MA = input d / output d or MA ramp = Ramp Length / Ramp Height Efficiency = useful work output / total work input, or Efficiency = actual MA / theoretical MA (usually represented as a percent, x100 = %)

Machines Conservation of Energy – F d = F d Levers

Machines MA ramp = Ramp Length / Ramp Height MA = 5 / 1 = 5 MA = input arm length / output arm length

Mechanical Energy Mechanical Energy (E) – is equal to the sum of kinetic energy and potential energy if no other forms of energy are present. E = KE + PE Conservation of energy E i = E f, so KE i + PE i = KE f + PE f i = initial, f = final