Kinetic and potential energies — OCR A-Level Physics
Test yourself on Kinetic and potential energies with OCR A-Level practice questions.
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Kinetic and potential energies explained
Kinetic energy is the energy an object possesses due to its motion.
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For an object of mass m moving at speed v, the kinetic energy Ek is given by Ek = 1/2 mv². The equation shows that kinetic energy depends on the mass and on the square of the speed. Doubling the speed quadruples the kinetic energy, while doubling the mass only doubles it. The unit of energy is the joule (J), where 1 J = 1 kg m² s⁻². When using the equation, ensure mass is in kilograms and speed in metres per second. For example, a 2 kg object moving at 3 m s⁻¹ has Ek = 1/2 × 2 × 3² = 9 J. In MCQ questions, you may need to calculate kinetic energy, compare values, or identify the effect of changing mass or speed.
(b) gravitational potential energy of an object in a uniform gravitational field; E p = mgh
Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. In a uniform gravitational field, such as near the Earth's surface, the change in GPE when an object of mass m is raised by a height h is given by Ep = mgh, where g is the gravitational field strength (approximately 9.81 N kg⁻¹ on Earth). The equation assumes the field is uniform, meaning g is constant over the height moved. The unit of GPE is the joule (J). For example, lifting a 2 kg mass by 3 m gives Ep = 2 × 9.81 × 3 = 58.86 J. In MCQ questions, you may calculate GPE, compare changes, or identify the effect of changing mass, height, or gravitational field strength.
(c) the exchange between gravitational potential energy and kinetic energy.
In a closed system where only gravity acts, gravitational potential energy (GPE) and kinetic energy (KE) can be exchanged. As an object falls, it loses GPE and gains KE; as it rises, it gains GPE and loses KE. If air resistance is negligible, the total mechanical energy (GPE + KE) remains constant. For example, a ball dropped from height h converts all its initial GPE (mgh) into KE just before impact, so 1/2 mv² = mgh, giving v = √(2gh). In MCQ questions, you may be asked to identify energy changes, calculate speeds using conservation of energy, or compare energies at different points.
Your focus
- Recall and apply the equation Ek = 1/2 mv² to calculate kinetic energy.
- Explain how kinetic energy depends on mass and speed, including the squared relationship with speed.
- Use the correct unit of energy (joule) and convert between units where necessary.
Show all 9 objectives
- Recall and apply the equation Ep = mgh to calculate gravitational potential energy changes.
- Explain the conditions under which the equation is valid, specifically a uniform gravitational field.
- Use the correct unit of energy and interpret the meaning of g in the equation.
- Describe the interchange between gravitational potential energy and kinetic energy during motion.
- Apply the principle of conservation of mechanical energy to solve problems involving falling or rising objects.
- Derive and use the relationship v = √(2gh) for an object falling from rest in a uniform gravitational field.
Kinetic and potential energies exam tips
Marking Points
- Kinetic energy is the energy possessed by an object due to its motion.
- The kinetic energy of an object is calculated using Ek = 1/2 mv², where m is mass in kg and v is speed in m s⁻¹.
- Kinetic energy is directly proportional to mass and to the square of speed.
- The unit of kinetic energy is the joule (J), equivalent to kg m² s⁻².
- When speed doubles, kinetic energy increases by a factor of four; when mass doubles, kinetic energy doubles.
- Gravitational potential energy is the energy stored in an object due to its position in a gravitational field.
- In a uniform gravitational field, the change in gravitational potential energy is calculated using Ep = mgh.
- m is mass in kg, g is gravitational field strength in N kg⁻¹, and h is vertical height change in m.
- The unit of gravitational potential energy is the joule (J).
- The equation applies when the gravitational field is uniform, i.e., g is constant over the change in height.
- Gravitational potential energy can be converted into kinetic energy and vice versa.
- In the absence of resistive forces, the total mechanical energy (sum of GPE and KE) is conserved.
- The exchange is described by equating the loss in GPE to the gain in KE: mgh = 1/2 mv².
- The speed of a falling object can be found from v = √(2gh) when starting from rest and ignoring air resistance.
- Energy conservation applies to systems where only conservative forces (like gravity) do work.
Examiner Tips
- 💡In multiple-choice questions, check whether the options involve squaring the speed; eliminate any that do not reflect the v² dependence.
- 💡If a question asks for the effect of changing speed, remember that kinetic energy is proportional to v², so a 3× increase in speed gives a 9× increase in kinetic energy.
- 💡Always write down the equation and substitute values with units to avoid errors; this also helps you check the unit of the answer.
- 💡In multiple-choice questions, check whether the height is vertical; if an object moves along a slope, you must use the vertical height, not the slope length.
- 💡If the question gives g as 10 N kg⁻¹, use that value; otherwise use 9.81 N kg⁻¹.
- 💡Remember that gravitational potential energy is relative to a chosen zero level; the equation gives the change in GPE.
- 💡In multiple-choice questions, look for options that conserve total energy; eliminate any that suggest energy is created or destroyed.
- 💡If a question involves a falling object, you can often use mgh = 1/2 mv² to find speed without knowing the mass.
- 💡Check whether the system is isolated; if friction or air resistance is present, mechanical energy is not conserved.
Common Mistakes
- Forgetting to square the speed: using v instead of v² in the equation. Correction: always square the speed before multiplying by mass and 1/2.
- Using mass in grams instead of kilograms: this leads to an incorrect energy in joules. Correction: convert mass to kg by dividing by 1000 if necessary.
- Confusing kinetic energy with momentum: momentum is mv, while kinetic energy is 1/2 mv². Correction: check the equation and units; momentum has units kg m s⁻¹, energy has units J.
- Incorrectly calculating 1/2 mv² by multiplying m by v first and then squaring the product. Correction: square the speed first, then multiply by mass and 1/2.
- Using the wrong value for g: for example, using 10 m s⁻² instead of 9.81 N kg⁻¹ when the question expects the standard value. Correction: check the question for the value of g to use; if not given, use 9.81 N kg⁻¹.
- Forgetting that h is the vertical height change, not the distance moved along a slope. Correction: always use the vertical component of displacement.
- Mixing up mass and weight: using weight (mg) in place of mass m in the equation. Correction: ensure you use mass in kg, not weight in N.
- Assuming the equation applies in non-uniform fields: Ep = mgh is only valid when g is constant. Correction: for large height changes, g varies and the equation is not accurate.
- Assuming energy is lost when it is only transferred between forms. Correction: in the absence of resistive forces, total mechanical energy is constant.
- Forgetting that mass cancels when equating mgh and 1/2 mv², leading to v = √(2gh). Correction: recognise that the final speed is independent of mass.
- Including air resistance in calculations when the question states it is negligible. Correction: only include resistive forces if explicitly mentioned.
- Mixing up the direction of energy transfer: for a rising object, KE is converted to GPE, not the other way around. Correction: identify whether the object is gaining or losing height.