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Wize University Physics Textbook (Master) > 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/s


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


The power could be also written as:

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




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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)

W=ΔUg=mgh=m(9.8)(12)W=\Delta U_g=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\ W

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

A tow car is towing a 900-kg car up on a 10∘10^{^{\circ}} 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.
Extra Practice
Practice: Power of a tow car
A tow car is towing a 900-kg car up on a 10∘10^{^{\circ}} 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.
The motion of a 1.00-kg box along the x-axis is described by the function x(t)=2.0−t2+0.5t3x\left(t\right)=2.0-t^2+0.5t^3. Which choice correctly represents the power delivered to the box as function of time?
A) P(t)=4t−9t2+4.5t3P\left(t\right)=4t-9t^2+4.5t^3 B) P(t)=1.5t−5t2+3t3P\left(t\right)=1.5t-5t^2+3t^3
C) P(t)=−4t−3t2−4.5t3P\left(t\right)=-4t-3t^2-4.5t^3 D) P(t)=4+3t2+4.5t3P\left(t\right)=4+3t^2+4.5t^3
work and power
Someone takes 11 minutes to walk up a hill 120m high. His weight is 550N.
(a) How much work did he do in climbing the hill?
(b) What power is developed by his muscles as he climbs?
power
A motor raises a mass of 3 kg to a height h at a constant speed of 0.05 m/s. The battery which provides energy to the motor originally stores 4 J of energy, all of which can be used to lift the mass.
(a) What is the power developed in the motor?
(b) To what maximum height can the motor lift the mass using its stored energy?
Power
A motorbike engine can develop a power of 90000 W in order to keep a constant velocity of 30 m/s. What is the pushing force?
Power
(a) How much work is done in lifting an object that weighs 250N to a height of 4m? (b) At what rate is work done if the 250N object is lifted to a height 4m in 4s?
A 1500-kg kg car accelerates from 0 to 10 m/s in 5 s with negligible friction and air resistance. What is the average power delivered by the engine? (1 hp=746 W)\left(1\ hp=746\ W\right)