IB Physics SLTopic A.3 โ Work, Energy & PowerPaper 1 & 2Power & Energy~6 min read
Power & Energy
Two machines can transfer exactly the same amount of energy and still behave completely differently โ because power is about how fast that energy gets transferred, not how much.
๐ What you need to know
Power is the rate at which energy is transferred, or the rate at which work is done
It’s calculated using P = ฮWโฮt
For a constant force moving something at constant velocity, power can also be found using P = Fv
Power is measured in watts (W), where 1 W = 1 J sโปยน
A higher-power device transfers the same energy in less time โ it doesn’t necessarily transfer more energy overall
What Is Power?
Power measures how quickly energy is transferred or work is done. It’s the time factor that separates two processes doing the same job at different speeds โ two elevators lifting identical loads to the same height are doing the same work, but the one that gets there faster has more power.
Power equationP = ฮWโฮt = Fv
Where P is power in watts, ฮW is the work done (or energy transferred) in joules, ฮt is the time interval in seconds, F is a constant force in newtons, and v is velocity in m sโปยน. The Fv version only applies when a constant force moves an object at a constant velocity, in the same direction as that force.
Both crates are lifted through the same height, doing the same work โ the higher-power lift simply gets there in less time
The Watt
Power is measured in watts (W). One watt is defined as a transfer of one joule of energy in one second.
Definition of the watt
1 W = 1 J sโปยน
Appliances are often given a power rating โ a kettle rated at 2000 W, for instance, transfers roughly 2000 joules of energy to its surroundings every second it’s switched on.
Quick recap: P = ฮW/ฮt for the general case; P = Fv when a constant force moves something at constant velocity. Power is about speed of transfer, not total amount.
WE 1
A crane’s engine exerts a constant force of 650 N while lifting a load through 250 m in 140 s. Calculate the average power developed by the engine.
Step 1 โ Calculate the work doneW = F ร d = 650 ร 250 = 162 500 JStep 2 โ Divide by timeP = 162 500 รท 140โ 1160 W โ 1.2 kW
WE 2
A delivery truck of mass 4200 kg travels at a constant 7.5 m sโปยน up a road inclined at 12ยฐ to the horizontal. Air resistance is negligible. Calculate the useful power developed by the engine to keep the truck moving at this speed.
Step 1 โ Find the force needed to overcome gravity along the slopeF = mg sin ฮธ = 4200 ร 9.8 ร sin(12ยฐ) โ 8560 NStep 2 โ Apply P = FvP = 8560 ร 7.5โ 64 000 W (2 s.f.)
๐ก Top tips
The Fv equation only works for a constant force at constant velocity โ accelerating objects need the general ฮWโฮt form instead
Make sure the force you use in P = Fv is acting in the same direction as the velocity
When a drag or resistive force is given, remember the driving force needed to maintain constant speed must be equal in size to overcome it
Keep energy (joules) and power (watts) clearly separate โ power is always energy divided by time
โ Common mistakes
Using P = Fv for a situation where the object is accelerating, rather than moving at constant velocity
Forgetting to resolve a force along a slope before using it in a power calculation
Treating a power rating as the amount of energy used, without multiplying by the time the device actually runs for
Mixing up power (rate of transfer) with work done (total amount transferred) when interpreting a question
Up next: Efficiency โ where we work out exactly how much of that power output actually ends up useful.
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