10 Work & Mechanical Energy
Resources
- Video to Watch: Mechanical Universe – Episode 14 – Potential Energy
- Extra Help: A-Level Physics Tutor
- Article to Read: Ultimate limit of human endurance found
Equations Introduced and Used in this Topic:
- Work [latex](W) = \vec{F}_{\text{net}} \cdot \vec{d}[/latex] or [latex]\vec{F}_{\text{net}} \vec{d} \cos ø[/latex]
- [latex]E_p = m g h[/latex]
- [latex]\Delta E_p = m g \Delta h[/latex]
- [latex]\Delta h = h_f - h_i[/latex]
- [latex]\Delta v = v_f - v_i[/latex]
- [latex]W = \Delta[/latex] Mechanical Energy
- [latex]E_k = \frac{1}{2} m v^2[/latex]
- [latex]\Delta E_k = \frac{1}{2} m \Delta v^2[/latex]
- [latex]V[/latex] or [latex]V_g = g h[/latex]
- [latex]w = m g[/latex]
(All equations are esolved as either scalar or vector)
Where…
- [latex]W[/latex] is Work, measured in joules (J)
- [latex]E_p[/latex] or [latex]\Delta E_p[/latex] is Gravitational Potential Energy or change in Gravitational Potential Energy, measured in joules (J)
- [latex]E_k[/latex] or [latex]\Delta E_k[/latex] is Kinetic Energy or change in Kinetic Energy, measured in joules (J)
- [latex]E[/latex] or [latex]\Delta E[/latex] is Energy or change in Energy, measured in joules (J)
- [latex]V[/latex] or [latex]V_g[/latex] is the Gravitational Potential, measured in newtons per kilogram (N/kg)
- [latex]m[/latex] is the Mass of the object, measured in kilograms (kg)
- [latex]g[/latex] or [latex]a_g[/latex] is the Gravitational Field Strength, measured in metres per second squared (m/s2)
- [latex]v[/latex] is the Speed of the object, measured in metres per second (m/s)
- [latex]v[/latex] or [latex]\Delta v[/latex] is the Speed or change in Speed of the object, measured in metres per second (m/s)
- [latex]v_f[/latex] & [latex]v_i[/latex] is the final and initial Speed of the object, measured in metres per second (m/s)
- [latex]F_{\text{net}}[/latex]is the Net Force or the Vector Sum of the Forces acting on a body or a system, measured in newtons (N)
- ø is the angle between the vectors of the Net Force and Displacement, measure in degrees (°)
- [latex]d[/latex] is the displacement through which the Net Force acts on a body or a System, measured in metres (m)
- [latex]h[/latex] or [latex]\Delta h[/latex] is the height or change in Vertical Height, measured in metres (m)
- [latex]h_f[/latex] & [latex]h_i[/latex] is the final and initial height of the object measured in metres (m)
Notes:
The Dot Product “[latex]\cdot[/latex]“ represents the cosine of the angle between two vectors. For Work it represents the angle between the direction of the Net Force and the displacement change.
The Cross Product “[latex]\times[/latex]“ represents the sine of the angle between two vectors. Equations using the cross product will be given later in your study of physics, such as the measure of Torque or the force on a charged particle moving in a magnetic field.
Work and Energy are measured in joules (J) or newton-metres (Nm)
For Example: Consider the following