10.3 - power

how can energy be transferred between different objects?

• work done

• heat transfer

• electromagnetic radiation

• electricity

• sound waves

how can energy be transferred by work done?

energy transferred by the force one object applies on another to move it

how can energy be transferred by heat transfer?

• due to conduction, convection, or radiation

• from a hot object to a cold one

in which sequence is thermal energy transferred?

from the hot object to the cold one

how can energy be transferred by electromagnetic radiation?

via light and radio waves

what is power?

• the rate of transfer of energy (i.e., the energy transferred per sec)

• P (in terms of energy) = Δ E / Δ T

• P (in terms of work done) = Δ W / Δ t

what does it mean for an object to be powerful?

it transfers energy in a short amount of time

what is the equation for power in terms of energy?

P = Δ E / Δ T

• P = power (rate of transfer of energy)

• Δ E = energy transferred

• Δ T = time taken for energy to be transferred

  
  

what is the equation for power in terms of work done?

P = Δ W / Δ t

• P = power (rate of transfer of work being done)

• Δ W = work done

• Δ t = time taken for work to be done

P = Δ E / Δ T

the rate of transfer of energy (power in terms of energy)

P = Δ W / Δ t

the rate of work being done (power in terms of work done)

why is power in terms of work done P = Δ W / Δ t ?

• P = Δ E / Δ t

• Δ E (energy transferred) = work done by force

• therefore rate of transfer of energy = work done per second

• therefore P = Δ W / Δ t

which variants of power can we measure?

• muscle power

• electrical power

• engine power

how do we measure muscle power?

• time how long it takes you to walk up a flight of steps

• know your weight and total height gain of flight of steps

• gain of potential energy = your weight x total height gain

• therefore muscle power = energy transferred / time taken = work done in a given force / time taken = (m g Δ h ) / t

• divide by two to find power output of each leg

(m g Δ h ) / t

muscle power

what is the equation for muscle power?

(m g Δ h ) / t

• m g = your weight

• Δ h = total height gain of a flight of stairs

• t = time taken to walk up the flight of stairs

if someone works out their total muscle power to be 400 W after walking up a flight of stairs, is this correct?

while this is correct, we have two legs (hopefully), so each leg would have a power of 400 W / 2 = 200 W

what is something to consider about total power output?

the number of output sources

why does the number of output sources matter when measuring total power output?

it could be misunderstood that each, for example, step we take is 400 W of power, when instead that is the total power when using our two legs (two output sources)

how do we find the total power output of one output source?

total power output / number of output sources

total power output / number of output sources

total power output of one output source, when there are multiple output sources

how do we measure electrical power?

• using a joulemeter

• joulemeter is read before and after light bulb is switched on

• difference between readings = energy supplied to light bulb

• electrical power = energy supplied to light bulb / time taken in the measured interval

what is used to measure the electrical power?

a joulemeter

what does a joulemeter do?

show the variance in joules of an electrical component

what is the equation for electrical power?

P = Δ E / Δ t

• P = electrical power

• Δ E = energy supplied to electrical component

• Δ t = time taken in the measured interval

energy supplied to electrical component / time taken

electrical power

what is the output power of an engine?

the motive power / work done by the engine per second

what is the work done by the engine of a powered object per second?

the motive power / output power

what are the forces at play when a powered object moves at constant velocity at constant height?

F_R = m g

resistive forces (friction, drag) are equal and opposite (balanced) to the motive force

here

when are the forces acting on a powered object balanced?

when the object moves at constant velocity at constant height

what happens to the work done by the engine of a powered object?

its transferred into the internal energy of the surroundings by the resistive forces

what is the work done by the engine of a powered object transferred to?

into the internal energy of the surroundings

what is the work done by the engine of a powered object transferred by?

the resistive forces (friction, drag)

what is the power output of the engine of a powered object?

P = F v

• P = motive power

• F = constant driving force from the engine

• v = constant speed of the vehicle

P = F v

motive power (power output of a powered vehicle)

when does P = F v apply?

when both the force F and speed V are constant

why is the power output of the engine of a powered object P = F v?

is the power output the same as work done?

what are the forces at play when a powered object gains speed?

output force > resistive forces

output force > resistive forces

forces at play for a powered object gaining speed

what does the work done by the engine of a powered object per sec do to the vehicle’s speed?

increase it

what increased a powered object’s speed?

the output power, if output force > resistive forces

the output power from the engine increases a powered object’s speed, providing what?

output force > resistive forces

why does the output power of a powered object increase the object’s speed?

• output power = work done by the engine per sec

• work done by engine per sec increases the E_k of the vehicle

• therefore output power increases powered object’s speed

why, for a powered object gaining speed, is output force > resistive forces?

• forces are balanced when an object is in constant velocity, therefore there must be a resultant for acceleration (i.e., change of speed) to occur

• output power = work done by engine per sec

• work done increases the E_k of the vehicle, enabling it to overcome the resistive forces acting on it

• therefore output force > resistive forces

what happens to the speed of a powered object when its output force exceeds the resistive forces?

it speeds up

what happens to the speed of a powered object when its resistive forces exceed its output force?

it slows down

what is the motive power of a powered object?

motive power = energy per sec wasted due to the resistive force + gain of E_k per sec

energy per sec wasted due to the resistive force + gain of E_k per sec

motive power of a powered object

why does the motive power of a powered object = energy per sec wasted due to the resistive force + gain of E_k per sec

• forces are balanced when an object is in constant velocity, therefore there must be a resultant for acceleration (i.e., change of speed) to occur

• output power = work done by engine per sec

• work done increases the E_k of the vehicle, enabling it to overcome the resistive forces acting on it

• so output force > resistive forces

• resistive forces increase internal energy of the surroundings

• therefore motive power of a powered object = energy per sec wasted due to the resistive force + gain of E_k per sec (why add?)

how do resistive forces effect energy?

they increase the internal energy of the surroundings

what increases the internal energy of the surroundings?

resistive forces

what is regulated in UK vehicles (trucks)?

• weight

• output power

why is truck weight and output power regulated?

to prevent damage to roads and bridges

what is the weight limit for trucks in the UK?

44 tonnes

what is the output power limit for trucks in the UK?

6 kW