Recall and use the equation for the change in gravitational potential energy ΔE_p = m g Δh

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IGCSE Physics - Energy (Gravitational Potential Energy)

IGCSE Physics 0625

1.7.1 Energy

Objective: Recall and use the equation for the change in gravitational potential energy ΔE_p = m g Δh

This section focuses on gravitational potential energy, a form of energy stored by an object due to its position in a gravitational field. We will learn how to calculate the change in gravitational potential energy when an object moves vertically.

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy an object possesses due to its height above a reference point. The formula for calculating GPE is:

$$E_p = m g h$$

Where:

  • $E_p$ = Gravitational potential energy (measured in Joules, J)
  • $m$ = Mass of the object (measured in kilograms, kg)
  • $g$ = Acceleration due to gravity (approximately 9.8 m/s2 near the Earth's surface)
  • $h$ = Height of the object above the reference point (measured in meters, m)

The change in gravitational potential energy (ΔEp) is the difference in GPE between two positions.

The Equation for Change in Gravitational Potential Energy

When an object moves vertically, the change in its gravitational potential energy is given by the following equation:

$$\Delta E_p = m g \Delta h$$

Where:

  • $\Delta E_p$ = Change in gravitational potential energy (measured in Joules, J)
  • $m$ = Mass of the object (measured in kilograms, kg)
  • $g$ = Acceleration due to gravity (approximately 9.8 m/s2)
  • $\Delta h$ = Change in height (final height - initial height) (measured in meters, m)

This equation tells us that the change in GPE is directly proportional to the mass of the object and the acceleration due to gravity. It is also directly proportional to the change in height.

Example Calculation

Consider a 2 kg mass lifted to a height of 3 meters. Calculate the change in its gravitational potential energy.

Using the equation:

$$\Delta E_p = m g \Delta h$$

$$\Delta E_p = 2 \text{ kg} \times 9.8 \text{ m/s}^2 \times 3 \text{ m}$$

$$\Delta E_p = 58.8 \text{ J}$$

Therefore, the change in gravitational potential energy is 58.8 Joules.

Table Summary

Quantity Symbol Units
Gravitational Potential Energy $E_p$ Joules (J)
Mass $m$ Kilograms (kg)
Acceleration due to gravity $g$ m/s2
Height $h$ Metres (m)
Change in Gravitational Potential Energy $\Delta E_p$ Joules (J)
Change in Height $\Delta h$ Metres (m)
Suggested diagram: An object being lifted vertically, illustrating the change in height and the direction of gravitational force.