Work, Force and Powewr

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• • • Energy: Ability to do work
  • Measured in Joules (J)
• Work: $Fs$ = $Nm$

$E_k=\frac{1}{2}m{v}^2$

• in Joules (J)

$E_p=mgh$

• in Joules (J)

$E_m=E_p+E_k$

• In this topic (Motion), we are mostly interest in mechanical energy, i.e. $E_p+E_k$
• Energy is a conserved quantity

$E_{pinitial}+E_{kinitial}=E_{pfinal}+E_{kfinal}$

• We will assume that total mechanical energy(TME) of an object in motion(includes at rest) is a constant

$Work=\Delta Energy=Fs$

$Work=\Delta Energy=Fscos(\theta )$

• **************************Where $\theta$ is the angle it makes with the ground
• Force in Newtons, Displacement in Meters

$Work=\frac{1}{2}m(v^2-u^2)$

• This is only for objects with no change in gravitational potential energy

$Work=\frac{1}{2}m(v-u)$

• Change in gravitational energy and kinetic energy
• In order for work to be considered to have been done on an object by a force, then the displacement of the object has to be at least, in part, in the direction of the applied force
• If the motion is perpendicular to the applied force and remains so, no work is done

Power

• Rate at which work is done

$\frac{J}{t}=\frac{\Delta E}{t}=W(watts),J{s}^{-1}$

• Work over time$Power=F{v}_{av}$