physics-class-11-unit-05-chapter-04-forces-on-bodies-systems-involving-strings-or-springs-lecture4-8-fbsjbcplx-s

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Fluid Friction </primary>
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- What happens if the contact of a solid body is with a fluid and by a fluid <span style="color:green">(liquid or gas)</span>.

- The surrounding liquid applies tangential force on the solid.

- The term used for the fluid friction: <span style="color:green">Drag force.</span>

- Fluid could also exert a force in a direction perpendicular to the velocity: <span style="color:blue">Buoyancy force or a vertical force.</span>

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<footer style = "font-size: 18px">Forces on Bodies Systems Involving Strings or Springs $\rightarrow$ Laws of Friction $\rightarrow$ <span style = "color:blue"> Fluid Friction </span> $\rightarrow$ Solid Friction $\rightarrow$ Force </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Force </primary>
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- External force on a body they could either be constant or they could be a function of distance.

- $\Rightarrow$ Electrostatics force
 
- $\Rightarrow$ Gravity

- Sum of external forces on the body: <span style="color:blue">$\vec F = m \vec a$</span>

- $\Rightarrow$ Function of velocity

- $\Rightarrow$ Function of time

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-05-chapter-04-forces-on-bodies-systems-involving-strings-or-springs-4_8-fbsjbcplx_s-085-0478.8.jpg)

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<footer style = "font-size: 18px">Fluid Friction $\rightarrow$ Solid Friction $\rightarrow$ <span style = "color:blue"> Force </span> $\rightarrow$ Contact Force $\rightarrow$ Special Contact Force </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Special Contact Force </primary>
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- $F_{AB}$ is divided into two parts

* Normal reaction 
* Friction force <span style="color:blue">(tangental force)</span>

- $\Rightarrow$ <span style="color:green">String pulling the body </span> 
 
- The string exerts a force on the body in the direction of the string.

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<footer style = "font-size: 18px">Force $\rightarrow$ Contact Force $\rightarrow$ <span style = "color:blue"> Special Contact Force </span> $\rightarrow$ Tension Force $\rightarrow$ Tension Force </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Tension Force </primary>
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- Force which sting exerts on the body = <span style="color:green">Tension
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- String pulls the body with a force, <span style="color:blue">$T$ $\rightarrow$ Tension.</span>

- This tension is in the direction of the string.

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<footer style = "font-size: 18px">Contact Force $\rightarrow$ Special Contact Force $\rightarrow$ <span style = "color:blue"> Tension Force </span> $\rightarrow$ Tension Force $\rightarrow$ Tension Force </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Tension Force </primary>
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- <span style="color:blue">If compress the string, then the string will just fold and it will not exert any force on the body. </span>
	
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<footer style = "font-size: 18px">Special Contact Force $\rightarrow$ Tension Force $\rightarrow$ <span style = "color:blue"> Tension Force </span> $\rightarrow$ Tension Force $\rightarrow$ Spring </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Tension Force </primary>
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- <span style="color:green">We have a string which ties two bodies </span>

- We make two assumptions:

- a)  string is light,

- <span style="color:blue">$\operatorname{Mass} \approx 0$</span>

- b) The string length does not change.
	
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<footer style = "font-size: 18px">Tension Force $\rightarrow$ Tension Force $\rightarrow$ <span style = "color:blue"> Tension Force </span> $\rightarrow$ Spring $\rightarrow$ Spring </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Spring </primary>
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- Force is needed to pull spring.

- <span style="color:blue">Compress the spring</span> $\rightarrow$ A force is needed to compress the spring.

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

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Spring </primary>
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- <span style="color:green">$F_{spring} = -kx$</span>

- Where:

- <span style="color:blue">k = Spring constant</span>

-  $x$   is the change in length of spring w.r.t. its unstretched length.

-  Negative indicate force is opposite to the direction of displacement.
	
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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-05-chapter-04-forces-on-bodies-systems-involving-strings-or-springs-4_8-fbsjbcplx_s-226-1246.8.jpg)

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<footer style = "font-size: 18px">Spring $\rightarrow$ Spring $\rightarrow$ <span style = "color:blue"> Spring </span> $\rightarrow$ Problem Solving Using Laws of Mechanics $\rightarrow$ Free Body Diagram of system </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Free Body Diagram of system </primary>
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- <span style="color:blue">FBD(Free Body Diagram)</span> of the single body.

- Isolate the body in question.

- We show a natural diagram of the body.

- Show all external forces acting on the body.

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<footer style = "font-size: 18px">Spring $\rightarrow$ Problem Solving Using Laws of Mechanics $\rightarrow$ <span style = "color:blue"> Free Body Diagram of system </span> $\rightarrow$ FBD of block $\rightarrow$ Contact force </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> FBD of block </primary>
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- a) Force acting from a distace.

- <span style="color:blue">Gravity $\rightarrow$ Weight</span>.

- <span style="color:green">$w=m g$</span>

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<footer style = "font-size: 18px">Problem Solving Using Laws of Mechanics $\rightarrow$ Free Body Diagram of system $\rightarrow$ <span style = "color:blue"> FBD of block </span> $\rightarrow$ Contact force $\rightarrow$ Free Body Diagram </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Contact force </primary>
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- Isolation of the body.

- Block is in contact with the ground.

- The effect of ground would be a normal force and a friction force.

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<footer style = "font-size: 18px">Free Body Diagram of system $\rightarrow$ FBD of block $\rightarrow$ <span style = "color:blue"> Contact force </span> $\rightarrow$ Free Body Diagram $\rightarrow$ Free Body Diagram </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Free Body Diagram </primary>
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- Suppose block lying on the ground and a string is tied to it.

- Draw the free body diagram of the block.

- There is a tension $T$ which is at an angle $\theta$.

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<footer style = "font-size: 18px">FBD of block $\rightarrow$ Contact force $\rightarrow$ <span style = "color:blue"> Free Body Diagram </span> $\rightarrow$ Free Body Diagram $\rightarrow$ Two Dimensional Problems </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Free Body Diagram </primary>
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- <span style="color:blue">FBD of block on ground with string attached.</span>

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<footer style = "font-size: 18px">Contact force $\rightarrow$ Free Body Diagram $\rightarrow$ <span style = "color:blue"> Free Body Diagram </span> $\rightarrow$ Two Dimensional Problems $\rightarrow$ Two Dimensional Problems </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Two Dimensional Problems </primary>
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- In 1D you will have only one direction and in 2d there will be two directions.

- Show $x$ and $y$ axes on the FBD.

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<footer style = "font-size: 18px">Free Body Diagram $\rightarrow$ Free Body Diagram $\rightarrow$ <span style = "color:blue"> Two Dimensional Problems </span> $\rightarrow$ Two Dimensional Problems $\rightarrow$ Two Dimensional Problems </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Two Dimensional Problems </primary>
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- $x$ and $y$ need not be along horizontal or vertical.

- They can be along on incline or at an angle.

- $ x $ and   $ y$   perpendicular.

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<footer style = "font-size: 18px">Free Body Diagram $\rightarrow$ Two Dimensional Problems $\rightarrow$ <span style = "color:blue"> Two Dimensional Problems </span> $\rightarrow$ Two Dimensional Problems $\rightarrow$ Two Dimensional Problems </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Two Dimensional Problems </primary>
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- <span style="color:green"><ins>FBD</ins></span>: show all the forces on the body

- <span style="color:blue">$ \vec{F}= m \vec{a} $</span>

- F along $x$  and  $y$

- <span style="color:blue"> $\vec{F}$</span> sum of all force acting on body

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-05-chapter-04-forces-on-bodies-systems-involving-strings-or-springs-4_8-fbsjbcplx_s-407-2049.6.jpg)

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<footer style = "font-size: 18px">Two Dimensional Problems $\rightarrow$ Two Dimensional Problems $\rightarrow$ <span style = "color:blue"> Two Dimensional Problems </span> $\rightarrow$ Two Dimensional Problems $\rightarrow$ Problem </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Two Dimensional Problems </primary>
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- $W$ = $mg$
	
- $\Sigma F_x = m a_x $

- $\Sigma F_y=m a_y$

- LHS comes from FBD

- <span style="color:blue">RHS  $\leftarrow$   Kinematics</span>

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### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Problem </primary>
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- $T$ is given, find accelaration of block?

- <span style="color:green"> <ins>Draw FBD</ins></span>

- $\Sigma F_x =T \cos \theta-f =  m a_x =m a $

- $\Sigma F_y  =  N+T \sin \theta-W=m a_y $

- $ N+T \sin \theta=W=m g=0$

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<footer style = "font-size: 18px">Two Dimensional Problems $\rightarrow$ Two Dimensional Problems $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Body is Slipping $\rightarrow$ Body is Slipping </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Body is Slipping </primary>
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- If the body is slipping then force of friction,

- $f=\mu_k N$

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<footer style = "font-size: 18px">Two Dimensional Problems $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Body is Slipping </span> $\rightarrow$ Body is Slipping $\rightarrow$ Slip </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Block is at rest </primary>
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- $\vec{a}=0$

- $ \Sigma F_x=0$

- $ \Sigma F_y=0 $

- $ N =  W$

- $f = 0 $

- So in this case there is no friction force acting on the block.

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<footer style = "font-size: 18px">Body is Slipping $\rightarrow$ Slip $\rightarrow$ <span style = "color:blue"> Block is at rest </span> $\rightarrow$ Block on the Table $\rightarrow$ Block on the Table </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Block on the Table </primary>
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- The table accelerates with an acceleration a $\rightarrow$ <span style="color:green">Block is not slipping table.</span>

- Acceleration a  given.

- What is friction force on the block?

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<footer style = "font-size: 18px">Slip $\rightarrow$ Block is at rest $\rightarrow$ <span style = "color:blue"> Block on the Table </span> $\rightarrow$ Block on the Table $\rightarrow$ Block on the Table </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Block on the Table </primary>
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- <span style="color:blue"> Accelaration of block = $a \hat{i} $</span>

- $\Sigma F_y=0 \Rightarrow N=W $

- $ \Sigma F_x=m a $

- <span style="color:green">$\Rightarrow-f=m a $</span>

- $f=-m a$, f is in right direction.

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<footer style = "font-size: 18px">Block is at rest $\rightarrow$ Block on the Table $\rightarrow$ <span style = "color:blue"> Block on the Table </span> $\rightarrow$ Block on the Table $\rightarrow$ Block on the Table </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Block on the Table </primary>
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- f =  ma

- Max. value of a for which block does not slip on table.

- $\mu_sN$  = ma

- $\mu_sW$   =  ma

- $W = mg$

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<footer style = "font-size: 18px">Block on the Table $\rightarrow$ Block on the Table $\rightarrow$ <span style = "color:blue"> Block on the Table </span> $\rightarrow$ Block on the Table $\rightarrow$ Block on the Table </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Block on the Table </primary>
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- $ f  =\mu_k N =\mu_k m g$

- $ m a=f $

- 'a' of block in ground frame

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### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Block Kept on an Inclined Plane </primary>
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- $\mu_s \rightarrow$ How to find

- $\theta=0^{\circ}$, Raise value of $\theta$

- At on angle $\theta_s$, Block starts to slip.

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<footer style = "font-size: 18px">Block on the Table $\rightarrow$ Block on the Table $\rightarrow$ <span style = "color:blue"> Block Kept on an Inclined Plane </span> $\rightarrow$ Friction Force $\rightarrow$ First Case </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> First Case </primary>
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- $\theta  <\theta_s $
- Along the x direction: $W \sin(\theta)$
- Along the y direction: $W \cos(\theta)$

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<footer style = "font-size: 18px">Block Kept on an Inclined Plane $\rightarrow$ Friction Force $\rightarrow$ <span style = "color:blue"> First Case </span> $\rightarrow$ Second Case $\rightarrow$ Third Case </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Second Case </primary>
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- $\theta=\theta_s $ 
- $ f=\mu_s N $

- $ W \sin \theta=\mu_s w \cos \theta $

- $ \mu_s=\frac{\sin \theta}{\cos \theta}=\tan \theta$

- <span style="color:green">< $\theta_s$ : block is at rest:</span>

- $N=w \cos \theta $

- $f=w \sin \theta$

- $a_x, a_y=0$

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<footer style = "font-size: 18px">Friction Force $\rightarrow$ First Case $\rightarrow$ <span style = "color:blue"> Second Case </span> $\rightarrow$ Third Case $\rightarrow$ Thank you </footer>

### <Success style="font-size:25px"> Forces On Bodies Systems Involving Strings Or Springs L-4 </Success>
### <primary style="font-size:24px"> Third Case </primary>
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- <span style="color:blue">$\theta>\theta_s$</span>

- Block accelerats down the inclne with accleration

- <span style="color:green">$N=W \cos \theta$</span>

- $W \sin \theta-\mu_k W \cos \theta=m a$

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<footer style = "font-size: 18px">First Case $\rightarrow$ Second Case $\rightarrow$ <span style = "color:blue"> Third Case </span> $\rightarrow$ Thank you $\rightarrow$  </footer>