Work, Energy, and Power: Fundamental Principles in A-Level Science
What Is Work?
Work is done when a force causes an object to move in the direction of the force:
W=FdcosθW = Fd \cos\thetaW=Fdcosθ
Where:
- WWW: Work (JJJ, Joules).
- FFF: Force (NNN).
- ddd: Displacement (mmm).
- θ\thetaθ: Angle between force and displacement.
Energy and Its Forms
Kinetic Energy (KEKEKE)
Energy of motion:
KE=12mv2KE = \frac{1}{2}mv^2KE=21mv2
Where:
- mmm: Mass (kgkgkg).
- vvv: Velocity (m/sm/sm/s).
Potential Energy (PEPEPE)
Energy due to position or height:
PE=mghPE = mghPE=mgh
Where:
- hhh: Height above reference (mmm).
Power (PPP)
Power is the rate at which work is done or energy is transferred:
P=WtP = \frac{W}{t}P=tW
Where:
- ttt: Time (sss).
Alternative forms include:
P=FvP = FvP=Fv
Conservation of Energy
Energy cannot be created or destroyed, only transformed or transferred.
Applications of Work, Energy, and Power
Transportation
Calculating power output for vehicles based on force and velocity.
Renewable Energy
Harnessing wind and solar energy through power calculations.
Engineering
Designing systems to minimize energy loss in power transmission.
Example Problem
A 50 kg50 \, \text{kg}50kg object is lifted 10 m10 \, \text{m}10m at a constant speed. Calculate the work done and power required if the lift takes 5 s5 \, \text{s}5s.
- Work:
W=mgh=50⋅9.8⋅10=4900 JW = mgh = 50 \cdot 9.8 \cdot 10 = 4900 \, \text{J}W=mgh=50⋅9.8⋅10=4900J
- Power:
P=Wt=49005=980 WP = \frac{W}{t} = \frac{4900}{5} = 980 \, \text{W}P=tW=54900=980W
Common Mistakes in Calculations
- Using incorrect angles in the work formula.
- Mixing up kinetic and potential energy.
- Ignoring units when calculating power.
Practice Questions
- A car of mass 1,000 kg1,000 \, \text{kg}1,000kg accelerates from rest to 20 m/s20 \, \text{m/s}20m/s. Calculate the work done on the car.
- Explain the significance of energy conservation in renewable energy systems.
- Describe one application of power calculations in engineering.
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