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5.2.1Forces and Motion

Gravitational Potential Energy

5 min read 7 parts Lesson 41 of 66 1 quiz Virtual lab

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Lesson summary

5.2.1 Gravitational Potential Energy — AS PHYSICS 9702 notes: Derive and use ΔEp = mgΔh for a uniform gravitational field.Definition — energy stored in a mass due to its position in a gravitational field.A mass that is lifted gains gravitational potential energy.A mass that falls…

  • Reference level
  • What the symbols mean
  • Against time
  • Gravitational field strength
  • Uniform field
  • Kinetic energy

Section 1 of 7Gravitational potential energy

Definition
  • Definition energy stored in a mass due to its position in a gravitational field.
  • A mass that is lifted gains gravitational potential energy.
  • A mass that falls loses gravitational potential energy.
Reference level
  • Reference level the potential energy at ground level on the Earth's surface is taken as zero.

Section 2 of 7Derivation of Ep = mgh

Lifting a mass m through a height h needs an upward force equal to its weight, mg.
The work done is W = Fs = mgh.
The lifted mass can now do extra work equal to mgh.
What the symbols mean:
This extra work equals the gain in gravitational potential energy, Ep = mgh.
What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)

Section 3 of 7The equation

Equation
  • ΔEp = mgΔh.
  • Ep is gravitational potential energy in joules (J).
  • m is mass in kilograms (kg).
  • g is gravitational field strength in N kg−1.
  • Δh is change in height in metres (m).
Validity
  • Validity the equation applies only to energy changes in a uniform gravitational field, such as near the Earth's surface.
  • In space, where the field is not uniform, this equation is not used.

Section 4 of 7GPE against height graphs

Shape
  • Shape a graph of GPE against height is a straight line, so GPE and height have a linear relationship.
Gradient
  • Gradient the gradient equals mg.
Against time
  • Against time the graph for a ball thrown upward or falling is identical in form when plotted against time.

Section 5 of 7More from the specification

1Potential energy and terminal speed
  • Potential energy and terminal speed converting gravitational potential into kinetic energy governs falling mass acceleration until drag forces limit terminal speed.
2Gravitational potential energy in uniform fields
  • In a uniform gravitational field near Earth's surface, the change in potential energy is given by Ep = mgh.
3Conservation of mechanical energy
  • In the absence of dissipative friction or air resistance, total mechanical energy is conserved, linking velocity change to vertical displacement.
4Work-energy theorem in non-uniform fields
  • Gravitational potential in radial fields is defined as work done per unit mass bringing a test mass from infinity: Vg = -GM/r.
5Gravitational potential energy in uniform fields
  • In a uniform gravitational field near Earth's surface, the change in potential energy is given by Ep = mgh.
6Conservation of mechanical energy
  • In the absence of dissipative friction or air resistance, total mechanical energy is conserved, linking velocity change to vertical displacement.
7Work-energy theorem in non-uniform fields
  • Gravitational potential in radial fields is defined as work done per unit mass bringing a test mass from infinity: Vg = -GM/r.
8Velocity
  • Rate of change of displacement.
9Displacement
  • Change in position.
10Newton
  • Unit of force, kg m s-2.
11Kinetic energy
  • K = ½mv2, energy of motion.
12Energy transferred
  • W = V Q, in joules.
    What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)

Section 6 of 7Key terms

TermMeaning
Gravitational potential energyEnergy stored in a mass because of its position in a gravitational field.
Gravitational field strengthForce per unit mass on a mass in a gravitational field, g, in N kg⁻¹.
Uniform fieldField with the same strength and direction at every point, as near the Earth’s surface.
Work doneForce multiplied by displacement in the direction of the force.

Section 7 of 7Exam technique

1
Using the distance along a slope — only the vertical height change counts.
2
Using the equation far from the Earth where g is not constant.
3
Forgetting that only changes in potential energy matter, not absolute values.
4
Mixing units — mass must be in kg and height in m.
Try it in the virtual labRoller coaster: energy and the loop \n