Wize High School Grade 12 Physics Textbook > Work and Energy

Power

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Power 

Power is defined as rate of energy generation or consumption or the rate at which work is done. 

The S.I unit for power is Watts.1 W=1 J/s1\ W=1\ J/s1 W=1 J/s

P=ΔEΔt         or        P=WorkTime\boxed{P=\frac{\Delta E}{\Delta t}\ \ \ \ \ \ \ \ \ or  \ \ \ \ \ \ \ \ P=\frac{Work}{Time}}P=ΔtΔE​         or        P=TimeWork​​

The power could be also written as: 

P=F ⃗. v⃗  =Fvcos⁡θ\boxed{P=\vec{F\ }.\ \vec{v}\ \ =Fv\cos\theta}P=F . v  =Fvcosθ​

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Example: Quick Power 

A bin of wood slabs is raised upwards through a vertical height of 12.0m at a constant velocity in 4.2 minutes by a crane with a power input of 30W. What is the mass of the wood?

Solution:

ΔK=0(Constant velocity)\Delta K=0\qquad (Constant\ velocity)ΔK=0(Constant velocity) 

W=ΔUg=mgh=m(9.8)(12)W=\Delta U_g=mgh=m(9.8)(12)W=ΔUg​=mgh=m(9.8)(12)

P=WΔt=m(9.8N/kg)(12m)4.2×60s=30 WP=\dfrac{W}{\Delta t}=\dfrac{m(9.8N/kg)(12m)}{4.2\times 60s}=30\ WP=ΔtW​=4.2×60sm(9.8N/kg)(12m)​=30 W

→m=75609.8(12)=64.3 kg\rightarrow\quad m=\frac{7560}{9.8(12)}=64.3\ kg→m=9.8(12)7560​=64.3 kg

A tow car is towing a 900-kg car up on a 10∘10^{^{\circ}}10∘ hill with constant speed of 36 km/h. The hill is sandy and exerts constant friction force of 300 N on the car. How much power does the tow car supply to tow the car? Select the closest answer.