physics-class-11-unit-06-chapter-04-work-energy-theorem-and-concept-of-potential-energy-lecture-4-6-hj27qknhwbu

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> Work Energy Theorem </primary>
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- $K=\frac{1}{2} m v^2$

- If a particle moves from position 1 to position 2, such that at position 1 its speed is $v_i$, and at position 2 the speed is $v_f$.

- Kinetic energy at 1 = $\frac{1}{2} m v_i^2$

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<footer style = "font-size: 18px"> $\rightarrow$ Work Energy Theorem and Concept of Potential Energy $\rightarrow$ <span style = "color:blue"> Work Energy Theorem </span> $\rightarrow$ Work Energy Theorem $\rightarrow$ Work Energy Theorem </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> Work Energy Theorem </primary>
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- $W$ = $K_f$ – $K_i$ = $\Delta K$

- W is work done by external forces acting on the particle as it moves from state 1 to state 2.

- Work done by external forces will be the work done by net external forces.

- $\sum \vec{F}_{i \text { ext. }}$.

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<footer style = "font-size: 18px">Work Energy Theorem $\rightarrow$ Work Energy Theorem $\rightarrow$ <span style = "color:blue"> Work Energy Theorem </span> $\rightarrow$ Work Energy Theorem $\rightarrow$ One-Dimensional Formulation </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> Work Energy Theorem </primary>
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- $K=\frac{1}{2} m v^2$

- **Differentiate with respect to time**,

* $\frac{d K}{d t}=\frac{1}{2} m \frac{d}{d t}\left(v^2\right)=\frac{1}{2} m 2v \frac{d v}{d t} = m\frac{d v}{d t} v$

* $\frac{d K}{d t} = F v$

* $v \rightarrow \frac{d x}{d t}$

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<footer style = "font-size: 18px">Work Energy Theorem $\rightarrow$ Work Energy Theorem $\rightarrow$ <span style = "color:blue"> Work Energy Theorem </span> $\rightarrow$ One-Dimensional Formulation $\rightarrow$ Work Energy Theorem </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
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* $\frac{d K}{d t} = F\frac{d x}{d t}$

* $\int_i^f d k=\int_{x_i}^{x_f} F d x$

* $\Delta K=W$

* Force is along one direction F $\rightarrow x$.

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<footer style = "font-size: 18px">Work Energy Theorem $\rightarrow$ Work Energy Theorem $\rightarrow$ <span style = "color:blue"> One-Dimensional Formulation </span> $\rightarrow$ Work Energy Theorem $\rightarrow$ Work Energy Theorem </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> Work Energy Theorem </primary>
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- The work energy theorem is valid for 2D or 3D motion.

* $K=\frac{1}{2} m(\vec{v} \cdot \vec{v})$

* $\frac{d K}{d t}=\frac{1}{2} m 2\left(\vec{v} \cdot \frac{d \vec{v}}{d t}\right)=\vec{v} \cdot m \frac{d \vec{v}}{d t}$

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<footer style = "font-size: 18px">Work Energy Theorem $\rightarrow$ One-Dimensional Formulation $\rightarrow$ <span style = "color:blue"> Work Energy Theorem </span> $\rightarrow$ Work Energy Theorem $\rightarrow$ Work Energy Theorem </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> No Work </primary>
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- There are forces which act on a particle but do no work.

- Work done by $F_1$ $=\int \overrightarrow{{F_1}} \cdot {d \vec{r}}$

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<footer style = "font-size: 18px">Work Energy Theorem $\rightarrow$ Work Energy Theorem $\rightarrow$ <span style = "color:blue"> No Work </span> $\rightarrow$ Normal Reaction $\rightarrow$ Circular Motion </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
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- A particle moves on a circular path.

- The particle is moving in a direction which is perpendicular to the string force.

- In case of circular motion, work done by T = 0.

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<footer style = "font-size: 18px">No Work $\rightarrow$ Normal Reaction $\rightarrow$ <span style = "color:blue"> Circular Motion </span> $\rightarrow$ Ball Being Thrown in Air $\rightarrow$ Ball Being Thrown in Air </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
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- Throw the ball up in air from ground with speed v.

- As the ball moves up gravity starts acting down, a point comes where v = 0.

- $K=\frac{1}{2} m v^2$

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<footer style = "font-size: 18px">Normal Reaction $\rightarrow$ Circular Motion $\rightarrow$ <span style = "color:blue"> Ball Being Thrown in Air </span> $\rightarrow$ Ball Being Thrown in Air $\rightarrow$ Ball Being Thrown in Air </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
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- <span style="color:green">At top position (highest)</span>

- v = 0, K = 0

- Now gravity increases the speed as the ball comes down,so kinetic energy increases.

- Gravity is doing work on the ball throughout.

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<footer style = "font-size: 18px">Circular Motion $\rightarrow$ Ball Being Thrown in Air $\rightarrow$ <span style = "color:blue"> Ball Being Thrown in Air </span> $\rightarrow$ Ball Being Thrown in Air $\rightarrow$ Ball Being Thrown in Air </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
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- <span style="color:green">**Downward motion**</span>
	
- Gravity is acting down and the displacement vector $\vec{r}$ is also down. So the work done is positive. w > 0

- $\Delta K = W > 0$

- The kinetic energy starts to increase.

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<footer style = "font-size: 18px">Ball Being Thrown in Air $\rightarrow$ Ball Being Thrown in Air $\rightarrow$ <span style = "color:blue"> Ball Being Thrown in Air </span> $\rightarrow$ Block and Spring $\rightarrow$ Block and Spring </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
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- Block sliding on a frictionless surface and encountering a spring.

- It touches the spring.

- Compresses the spring, spring applies an opposite force on the block.

- Velocity of the block decreases, because of spring.

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<footer style = "font-size: 18px">Ball Being Thrown in Air $\rightarrow$ Ball Being Thrown in Air $\rightarrow$ <span style = "color:blue"> Block and Spring </span> $\rightarrow$ Block and Spring $\rightarrow$ Potential Energy </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> Block and Spring </primary>
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- Block of mass m slides on a surface with friction.

- Because of work done due to friction, the kinetic energy of the block $K=\frac{1}{2} m v^2 = 0$

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<footer style = "font-size: 18px">Ball Being Thrown in Air $\rightarrow$ Block and Spring $\rightarrow$ <span style = "color:blue"> Block and Spring </span> $\rightarrow$ Potential Energy $\rightarrow$ Potential Energy </footer>

### <Success style="font-size:25px"> Work Energy Theorem And Concept Of Potential Energy L-4 </Success>
### <primary style="font-size:24px"> Potential Energy </primary>
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- Concept of potential energy is applicable only to those forces whose work is stored as energy.

- <span style="color:green">$\rightarrow$ conservative forces</span>

* $V(x)-V\left(x_0\right)=-\int_{x_0}^x F d x$

- **Differentiate:**

* $\frac{d V}{d x}=-F(x)$

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<footer style = "font-size: 18px">Potential Energy $\rightarrow$ Potential Energy $\rightarrow$ <span style = "color:blue"> Potential Energy </span> $\rightarrow$ Conservative Force $\rightarrow$ Conservative Force </footer>