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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power3 Marks
Question
Work done by a force is given by $\text{W}=\vec{\text{F}.}\vec{\text{S}}\text{ Where}\vec{\text{ F}}$ is the force and $\vec{\text{S}}$is the displacement. Show that:
  1. Work done is also equal to change in K.E.
  2. Work done is also equal to change in potential energy using this expression.
✓

Answer

  1.  

m = mass of body at rest
$\vec{\text{ds}}$ = small displacement in the direction of force Small amount of work done by force
$\text{dW}=\vec{\text{F}}.\vec{\text{ds}}$
$=\text{FdS}\cos0^\circ=\text{FdS}$
If is acceleration Produced in the body, then
$\vec{\text{F}}=\text{m}\vec{\text{a}}=\text{m}\frac{\text{dv}}{\text{dt}}$
$\text{dW}=\bigg(\text{m}\frac{\text{dv}}{\text{dt}}\bigg).\text{dS}=\text{m}\bigg(\frac{\text{dS}}{\text{dt}}\bigg)\text{dv}$
$=\text{mv}\text{ dv}$
Total work done by the force
$\text{W}=\int_\limits{0}^{\text{v}}\text{vdv}=\text{m}\bigg[\frac{\text{v}^2}{2}\bigg]_0^\text{v}$
$\text{W}=\frac{1}{2}\text{mv}^2$
  1. F = mg

As the distance is moved in the direction of force applied
Work done = Force distance
W = F × h = mgh

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