Work, Energy and Mechanical Power

Mechanical Engineering · CHAPTER 3 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Use energy conservation to estimate lifting work and power.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

Work transfers energy when a force acts through displacement. Power measures the rate of energy transfer. Choose a reference for gravitational potential energy and account for kinetic energy and losses. An efficiency calculation compares useful output with input using the same time interval.

2. Write the model

W = Fd; ΔEp = mgh; P = W/t; η = Pout/Pin

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

Lifting 50 kg through 2 m requires 981 J using g=9.81 m/s². Completing the lift in 5 s requires 196.2 W of useful average power. At 80% efficiency, input power is 245.25 W.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Lift time (s)	Useful power (W)	Input at 80% (W)
2	490.5	613.125
5	196.2	245.25
10	98.1	122.625

Change lift duration while keeping mass and height fixed. Energy stays constant; average power changes inversely with time.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

What useful energy is needed to lift 100 kg by 2 m?

Reveal the answer and check your work

1962 J, ignoring losses.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Power in kW and energy in kWh are not interchangeable.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.