Edexcel iGCSE Physics -4.15 Conservation of Energy in Mechanical Systems- Study Notes- New Syllabus
Edexcel iGCSE Physics -4.15 Conservation of Energy in Mechanical Systems- Study Notes- New syllabus
Edexcel iGCSE Physics -4.15 Conservation of Energy in Mechanical Systems- Study Notes -Edexcel iGCSE Physics – per latest Syllabus.
Key Concepts:
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Link Between Gravitational Potential Energy, Kinetic Energy and Work Done
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another.
This principle creates a direct link between gravitational potential energy, kinetic energy, and work done.
Energy Changes When an Object Falls
- An object raised above the ground has gravitational potential energy.
- As it falls, gravitational potential energy decreases.
- The lost gravitational potential energy is transferred into kinetic energy.
- If air resistance is negligible, total energy remains constant.
Loss of GPE = Gain in KE
Role of Work Done
When a force causes an object to move, work is done.
- Work done against gravity increases gravitational potential energy.
- Work done by gravity increases kinetic energy.
- Work done = energy transferred.
This means that work links forces to energy changes.
Key Relationships Used
Gravitational potential energy:
\( \mathrm{E_p = mgh} \)
Kinetic energy:
\( \mathrm{E_k = \dfrac{1}{2}mv^2} \)
Work done:
\( \mathrm{W = F \times s} \)
All three quantities are measured in joules (J).
Energy Transfer in Real Situations
- Falling objects: GPE → KE
- Lifting objects: work done → GPE
- Braking vehicles: KE → thermal energy (work done by friction)
If friction or air resistance is present, some energy is transferred to the thermal store, but total energy is still conserved.
Key Idea
- Energy is conserved at all times.
- Gravitational potential energy, kinetic energy and work are directly linked.
- Work done explains how energy is transferred.
Important Points to Remember
- Energy lost from one store equals energy gained by others.
- Ignoring air resistance simplifies calculations.
- Always use SI units.
Example
A ball of mass \( \mathrm{2.0\ kg} \) is dropped from a height of \( \mathrm{10\ m} \).
Calculate the speed of the ball just before it hits the ground. (Take \( \mathrm{g = 10\ N/kg} \). Ignore air resistance.)
▶️ Answer / Explanation
Initial gravitational potential energy:
\( \mathrm{E_p = mgh = 2.0 \times 10 \times 10 = 200\ J} \)
By conservation of energy:
\( \mathrm{E_k = 200\ J} \)
Use:
\( \mathrm{E_k = \dfrac{1}{2}mv^2} \)
\( \mathrm{200 = \dfrac{1}{2} \times 2.0 \times v^2} \)
\( \mathrm{v^2 = 200} \)
\( \mathrm{v = 14\ m/s\ (approx.)} \)
Example
A student lifts a \( \mathrm{5.0\ kg} \) box vertically through a height of \( \mathrm{2.0\ m} \).
(a) Calculate the work done by the student. (b) State the energy change that occurs.
▶️ Answer / Explanation
(a)
\( \mathrm{W = mgh = 5.0 \times 10 \times 2.0 = 100\ J} \)
(b)
The work done by the student is transferred into gravitational potential energy of the box.