Conservation of energy IB DP Physics Study Notes - 2025 Syllabus
Conservation of energy IB DP Physics Study Notes
Conservation of energy IB DP Physics Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand
- the principle of the conservation of energy
- that mechanical energy is the sum of kinetic energy, gravitational potential energy and elastic potential energy
- that in the absence of frictional, resistive forces, the total mechanical energy of a system is conserved
- that if mechanical energy is conserved, work is the amount of energy transformed between different forms of mechanical energy in a system, such as:
☐ the kinetic energy of translational motion as given by $E_k = \frac{1}{2}mv^2 = \frac{p^2}{2m}$
☐ the gravitational potential energy, when close to the surface of the Earth as given by $\Delta E_p = mg\Delta h$
☐ the elastic potential energy as given by $E_H = \frac{1}{2}k(\Delta x)^2$
Standard level and higher level: 8 hours
Additional higher level: There is no additional higher level content
- IB DP Physics 2025 SL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Physics 2025 HL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Physics 2025 SL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
- IB DP Physics 2025 HL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
The Principle of the Conservation of Energy
The principle of conservation of energy states that:
“Energy cannot be created or destroyed, only transformed from one form to another or transferred between objects. The total energy of a closed system remains constant.”
This principle is fundamental in physics and applies to all types of energy including:
- Kinetic energy
- Potential energy (gravitational, elastic, electric, etc.)
- Thermal energy
- Chemical, nuclear, and more
In a closed system, where no external forces or energy inputs exist, the total energy remains unchanged over time. However, it can change form, e.g., from kinetic energy to thermal energy or from chemical to mechanical.
Example:
A pendulum is released from rest at a certain height. As it swings down, describe how the conservation of energy applies.
▶️ Answer/Explanation
At the top: all energy is gravitational potential energy (GPE)
As it falls: GPE is converted into kinetic energy (KE)
At the bottom: GPE is minimum, KE is maximum
Total mechanical energy (GPE + KE) remains constant throughout the swing (assuming no air resistance or friction)
This illustrates the conservation of energy in a frictionless, closed system.
Mechanical Energy is the Sum of Kinetic Energy, Gravitational Potential Energy, and Elastic Potential Energy
The total mechanical energy of a system is defined as the sum of:
- Kinetic energy (EK) — energy due to motion
- Gravitational potential energy (EP) — energy due to position in a gravitational field
- Elastic potential energy (EH) — energy stored in stretched or compressed elastic materials (like springs)
So, the total mechanical energy \( E_{\text{mech}} \) of an object or system is given by:
\( E_{\text{mech}} = E_K + E_P + E_H \)
Where:
- \( E_K = \frac{1}{2}mv^2 \)
- \( E_P = mgh \)
- \( E_H = \frac{1}{2}kx^2 \)
\( m \): mass, \( v \): velocity, \( g \): gravitational field strength, \( h \): height above reference point, \( k \): spring constant, \( x \): displacement from spring’s natural length
These forms of energy may transform into one another, but their sum remains constant in the absence of resistive forces.
Example:
A 0.5 kg mass is attached to a spring (k = 200 N/m) and is compressed by 0.1 m. What is the total mechanical energy stored in the system at this point?
▶️ Answer/Explanation
Step 1: Use elastic potential energy formula
\( E_H = \frac{1}{2}kx^2 = \frac{1}{2}(200)(0.1)^2 = 1 \, \text{J} \)
Step 2: Object is at rest, and on the floor (no KE or GPE)
Total mechanical energy = \( E_K + E_P + E_H = 0 + 0 + 1 = \boxed{1 \, \text{J}} \)
This energy will convert into kinetic and potential energy as the spring oscillates.
In the Absence of Frictional or Resistive Forces, the Total Mechanical Energy of a System is Conserved
In an ideal (frictionless) system, where no non-conservative forces (like friction or air resistance) are present, the total mechanical energy remains constant throughout the motion of the system.
This means: \( E_{\text{mech(initial)}} = E_{\text{mech(final)}} \) or \( E_K + E_P + E_H = \text{constant} \)
As energy transforms between kinetic, gravitational potential, and elastic potential forms, their total sum does not change.
However, if friction or drag is present, mechanical energy is not conserved — some of it is transformed into non-mechanical forms such as heat or sound.
Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system.
(a) A system with only conservative forces. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air resistance) because the force in the spring is conservative. The spring can propel the rock back to its original height, where it once again has only potential energy due to gravity.
(b) A system with nonconservative forces. When the same rock is dropped onto the ground, it is stopped by nonconservative forces that dissipate its mechanical energy as thermal energy, sound, and surface distortion. The rock has lost mechanical energy.
Example:
A ball of mass \( 0.2 \, \text{kg} \) is dropped from a height of \( 5.0 \, \text{m} \). Assuming no air resistance, find the speed just before it hits the ground.
▶️ Answer/Explanation
Step 1: Use conservation of mechanical energy
Initial energy: \( E_P = mgh = 0.2 \cdot 9.8 \cdot 5 = 9.8 \, \text{J} \)
At the bottom, height = 0 → \( E_P = 0 \), all energy is kinetic
Step 2: Solve for speed using \( E_K = \frac{1}{2}mv^2 \)
\( 9.8 = \frac{1}{2}(0.2)v^2 \)
\( v^2 = \frac{9.8 \cdot 2}{0.2} = 98 \Rightarrow v = \boxed{9.9 \, \text{m/s}} \)
No mechanical energy was lost — only converted from potential to kinetic.
Energy Transformed Between Different Forms of Mechanical Energy in a System
In the absence of friction or resistance, when mechanical energy is conserved, the work done by internal conservative forces leads to transformation between:
- Kinetic energy \( E_K = \frac{1}{2}mv^2\quad \frac{p^2}{2m} \)
- Gravitational potential energy \( E_P = mgh \)
- Elastic potential energy \( E_H = \frac{1}{2}kx^2 \)
In such cases, no mechanical energy is added or removed from the system; it is only converted between these forms.
The total work done by conservative forces (like gravity or spring forces) simply causes a shift in energy from one mechanical form to another.
Example:
A block of mass \( 1.0 \, \text{kg} \) slides down a frictionless ramp of height \( 3.0 \, \text{m} \). Find its speed at the bottom of the ramp.
▶️ Answer/Explanation
Step 1: Mechanical energy at the top
At top: \( E_P = mgh = 1.0 \cdot 9.8 \cdot 3.0 = 29.4 \, \text{J} \)
\( E_K = 0 \)
Step 2: At the bottom
All energy is now kinetic:
\( \frac{1}{2}mv^2 = 29.4 \Rightarrow v^2 = \frac{2 \cdot 29.4}{1.0} = 58.8 \)
\( v = \boxed{7.67 \, \text{m/s}} \)
Conclusion:
The gravitational potential energy was transformed into kinetic energy as work done by gravity. No energy was lost to the surroundings.